市大数学教室

大阪市立大学数学研究所
(Osaka City University Advanced Mathematical Institute)
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Friday Seminar on Knot Theory(2011年度)
2010年度 2012年度
2011年度組織委員  森内 博正



講 演 者 :小畑 久美(大阪市立大学数学研究所(OCAMI))
タ イ ト ル :A generalization of an enumeration on cyclic automorphism graphs
for edge colored hypergraphs
(アブストラクト) (PDF)
日 時 :2月3日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :Chad Musick(名古屋大学)
タ イ ト ル :Recognizing Trivial Links in Polynomial Time
(アブストラクト) (PDF)
日 時 :2月3日(金)15:00~16:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :大城 佳奈子(日本女子大学)
タ イ ト ル :Minimal numbers of colors for surface-knots and quandle cocycle
invariants
(アブストラクト) (PDF)
日 時 :1月27日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :新庄 玲子(早稲田大学)
タ イ ト ル :On the collection of complementary faces associated to the diagrams of a link
(partially joint work with Colin C. Adams and Kokoro Tanaka)
(アブストラクト) (PDF)
日 時 :1月27日(金)15:00~16:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :Roland van der Veen (University of California, Berkeley)
タ イ ト ル :The many faces of the colored Jones polynomial
(アブストラクト) (PDF)
日 時 :12月16日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :中村 伊南沙(京都大学数理解析研究所)
タ イ ト ル :Unknotting numbers of torus-covering knots
(アブストラクト) (PDF)
日 時 :12月16日(金)15:00~16:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :高尾 和人(大阪大学)
タ イ ト ル :Heegaard splittings and singularities of product maps
(アブストラクト) (PDF)
日 時 :12月9日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :門田 直之(大阪大学)
タ イ ト ル :Sections of surface bundles and Lefschetz fibrations
(joint work with R. Inanc Baykur and Mustafa Korkmaz)
(アブストラクト) (PDF)
日 時 :11月25日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :岩切 雅英(佐賀大学)
タ イ ト ル :On $3$-component surface-links with braid index $4$
(アブストラクト) (PDF)
日 時 :11月18日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :三浦 嵩広(神戸大学)
タ イ ト ル :On flat braidzel surfaces for links
(アブストラクト) (PDF)
日 時 :11月11日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :矢口 義朗(広島大学)
タ イ ト ル :Homological invariants of systems of simple braids
(アブストラクト) (PDF)
日 時 :11月4日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :安部 哲哉(京都大学数理解析研究所(RIMS))
タ イ ト ル :Unoriented band-surgery on knots and links
(アブストラクト) (PDF)
日 時 :10月28日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :塚本 達也(大阪工業大学)
タ イ ト ル :Simple ribbon fusions for links
(アブストラクト) (PDF)
日 時 :10月21日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :船越 紫(奈良女子大学)
タ イ ト ル :On pseudo-fiber surfaces of level $n$
(アブストラクト) (PDF)
日 時 :10月7日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :野坂 武史 (京都大学数理解析研究所(RIMS))
タ イ ト ル :Quandle cocycle invariants of Lefschetz fibrations over the 2-sphere
(アブストラクト) (PDF)
日 時 :7月15日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :芦原 聡介(広島大学)
タ イ ト ル :Biquandle presentations of surface links from ch-diagrams
(アブストラクト) (PDF)
日 時 :7月8日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :小谷 賀子(奈良女子大学)
タ イ ト ル :A new bridge index for links with trivial knot components
(アブストラクト) (PDF)
日 時 :7月8日(金)15:00~16:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :田中 亮吉 (京都大学)
タ イ ト ル :Penner-Andersen's Fatgraph Models of Proteins
(アブストラクト) (PDF)
日 時 :7月1日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :金信 泰造 (大阪市立大学)
タ イ ト ル :Band surgery on 2-component links
(アブストラクト) (PDF)
日 時 :6月24日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :屋代 司 (Sultan Qaboos University)
タ イ ト ル :Cell-complexes for surface diagrams and Roseman moves
(アブストラクト) (PDF)
日 時 :6月17日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :今別府 孝規 (広島大学)
タ イ ト ル :On normalized arrow polynomials of checkerboard colorable virtual links
(アブストラクト) (PDF)
日 時 :6月10日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :栗屋 隆仁(大阪市立大学数学研究所(OCAMI))
タ イ ト ル :Mosaic quantum knots and related topics
(アブストラクト) (PDF)
日 時 :6月3日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :早野 健太(大阪大学)
タ イ ト ル :Classification of genus-1 simplified broken Lefschetz
(アブストラクト) (PDF)
日 時 :5月20日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :張 娟姫 (広島大学)
タ イ ト ル :Bridge presentations of links and Heegaard splittings of 3-manifolds
(アブストラクト) (PDF)
日 時 :5月13日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :田山 育男 (大阪市立大学数学研究所(OCAMI))
タ イ ト ル :Enumerating 3-manifolds with the first homology groups
isomorphic to (Z/nZ)+(Z/nZ) with lengths up to 10
(アブストラクト) (PDF)
日 時 :4月22日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :伊藤 哲也 (東京大学)
タ イ ト ル :Links having non-left orderable 2-fold branched coverings
(アブストラクト) (PDF)
日 時 :4月15日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop
講 演 者 :清水 理佳 (大阪市立大学数学研究所(OCAMI))
タ イ ト ル :Region crossing change is an unknotting operation
(アブストラクト) (PDF)
日 時 :4月8日(金)16:00~17:00
場 所 :数学 第3セミナー室(3153)
Toptop



アブストラクト集



講 演 者: 小畑 久美(大阪市立大学数学研究所(OCAMI))
タ イ ト ル: A generalization of an enumeration on cyclic automorphism graphs
for edge colored hypergraphs

We plan to give a generalization of Ohno's theorem for hypergraphs which gives a formula for enumeration on cyclic automorphism graphs with given number of vertices. We consider the enumeration in case of edge colored hypergraphs. This is a joint work with Yasuo Ohno.

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講 演 者: Chad Musick(名古屋大学)
タ イ ト ル: Recognizing Trivial Links in Polynomial Time

Trivial links are unique up to number of link components, but they can be hard to recognize from arbitrary diagrams. We define a measure, the crumple, on link diagrams and then demonstrate that for trivial links there is a sequence of moves by which the crumple may be strictly monotonically reduced. By our definition, the minimum possible crumple over all link diagrams is achieved only by embedding components disjointly in parallel planes, and so a link will be able to obtain this crumple if and only if it is trivial. The crumple is quadratic in the number of crossings, and we show that finding each reducing move takes only polynomial time and linear space. Therefore, we may decide whether a link is trivial in time polynomial on the number of crossings of a diagram of the link.
arXiv: 1110.2871v1 [math.GT]

Toptop



講 演 者: 大城 佳奈子(日本女子大学)
タ イ ト ル: Minimal numbers of colors for surface-knots and quandle cocycle
invariants

We study the minimal number of colors used for non-trivial Fox colorings of surface-knots. A lower bound for the minimal number is given by using quandle cocycle invariants. In particular, we show that the minimal number of the $2$-twist spinning of the $5_2$ knot for Fox 7-colorings is six. This is a joint work with Shin Satoh (Kobe University).

Toptop



講 演 者: 新庄 玲子(早稲田大学)
タ イ ト ル: On the collection of complementary faces associated to the diagrams of a link
(partially joint work with Colin C. Adams and Kokoro Tanaka)

Given a diagram of a link, one can ignore which strand is the overstrand at each crossing and think of it as a planar $4$-valent graph embedded on the $2$-sphere. This graph divides the sphere into $n$-gons, which we call faces. In this talk, we investigate the possibilities for the collection of complementary $n$-gon faces associated to the diagrams of a link.

Toptop



講 演 者: Roland van der Veen (University of California, Berkeley)
タ イ ト ル: The many faces of the colored Jones polynomial

In this talk we will discuss an elementary definition of the colored Jones polynomial for knots and show how it relates to many other aspects of knot theory. In particular we will give a survey of conjectures on the colored Jones polynomial including the volume conjecture and the AJ conjecture and report on recent progress.

Toptop



講 演 者: 中村 伊南沙(京都大学数理解析研究所)
タ イ ト ル: Unknotting numbers of torus-covering knots

A torus-covering knot is an oriented surface knot which is in the form of a covering over the standard torus. The unknotting number of an oriented surface knot $F$ is the minimal number of disjoint 1-handles necessary to deform $F$ to an unknotted surface knot by 1-handle surgery. In this talk we study unknotting numbers of torus-covering knots. In particular, we give examples of torus-covering knots with the unknotting number exactly $n$.

Toptop



講 演 者: 高尾 和人(大阪大学)
タ イ ト ル: Heegaard splittings and singularities of product maps

We give an upper bound for the Reidemeister-Singer distance between two Heegaard splittings in terms of the genera plus a somewhat unexpected number. It is unfortunately ambiguous but suggests that a certain development in singularity theory may lead to the best possible bound for the Reidemeister-Singer distance.

Toptop



講 演 者: 門田 直之(大阪大学)
タ イ ト ル: Sections of surface bundles and Lefschetz fibrations
(joint work with R. Inanc Baykur and Mustafa Korkmaz)

We will discuss the possible self-intersection numbers for sections of surface bundles & Lefschetz fibrations over surfaces, and the (un)boundedness of the number of critical points of a Lefschetz fibration with maximally self-intersecting sections, for fixed fiber and base genera. We will also calculate the stable commutator length of certain elements in the mapping class groups of surfaces with boundary.

Toptop



講 演 者: 岩切 雅英(佐賀大学)
タ イ ト ル: On $3$-component surface-links with braid index $4$

Any surface-links with braid index at most $3$ are ribbon, and any $m$-component surface-links with braid index $m$ are trivial $2$-links. There are examples of non-ribbon $1$- or $2$-component $2$-links with braid index $4$. In this talk, we show that any $3$-component surface-links with braid index $4$ are ribbon.

Toptop



講 演 者: 三浦 嵩広(神戸大学)
タ イ ト ル: On flat braidzel surfaces for links

Rudolph introduced a notion of braidzel surfaces as a generalization of pretzel surfaces in his study on quasipositivity for pretzel surfaces, and Nakamura showed that any oriented link has a braidzel surface as a Seifert surface for the link. In this talk, we introduce the notion of flat braidzel surfaces as a special kind of braidzel surfaces, and show that any oriented link has a flat braidzel surface. Moreover, we also introduce the genus and the crossing number of bands with respect to flat braidzel surfaces, and study their properties.

Toptop



講 演 者: 矢口 義朗(広島大学)
タ イ ト ル: Homological invariants of systems of simple braids

Hurwitz equivalence on systems of simple braids is studied, which can be used in the study of surface braids and surface links. In this talk, we define a matrix for a system of simple braids by using the first homology classes of a punctured disk. As applications, we give some invariants of surface braids by using the matrices obtained from the systems of their braid monodromies.

Toptop



講 演 者: 安部 哲哉(京都大学数理解析研究所(RIMS))
タ イ ト ル: Unoriented band-surgery on knots and links

A band-surgery is a local move on knots and links. It is well known that a band-surgery is an unknotting operation. In this talk, we survey some results on band-surgeries, and study how the orientability of a band-surgery relates to its unknotting sequences when we unknot a given knot by band-surgeries.
This is a joint work with Taizo Kanenobu.

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講 演 者: 塚本 達也(大阪工業大学)
タ イ ト ル: Simple ribbon fusions for links

We define and study special kinds of fusions, called simple ribbon fusions, for a link and a trivial link. A simple ribbon move, which we have previously worked on, is a simple ribbon fusion. Main theorem gives a sufficient condition for a knot obtained from the trivial knot by a simple fusion to be non-trivial. As a corollary, we show that the Kinoshita-Terasaka knot is non-trivial. This is a joint work with K.Kishimoto and T.Shibuya.

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講 演 者: 船越 紫(奈良女子大学)
タ イ ト ル: On pseudo-fiber surfaces of level $n$

The concept of pre-fiber surface in the 3-sphere $S^3$ was introduced by Kobayashi in [Ko]. In the paper, it is shown that any pre-fiber surface is transformed into a fiber surface by twisting is along arcs with certain properties. In this talk, we introduce pseudo-fiber surfaces of level $n$ for each non-negative integer $n$. (We note that a surface is a fiber surface if and only if it is a pseudo-fiber surface of level 0, and it is a pre-fiber surface if and only if it is a pseudo-fiber surface of level 1.) We show some fundamental properties of pseudo-fiber surfaces. Then we show that if an arc proper embedded in a pseudo-fiber surface of level $n$ satisfies certain properties, then the twist along the arc transforms it into a pseudo-fiber surface of level $n-1$. This gives a natural generalization of a result of Kobayashi's. Finally we propose an application of pseudo-fiber surface for giving an estimation of unknotting numbers of fibered knots.

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講 演 者: 野坂 武史 (京都大学数理解析研究所(RIMS))
タ イ ト ル: Quandle cocycle invariants of Lefschetz fibrations over the 2-sphere

We introduce quandle cocycle invariants of 4-dimensional Lefschetz fibrations over the 2-sphere, using quandle cocycles of Dehn quandles with non-abelian coefficients. In this talk, we first review a topological interpretation of quandle 2-cocycle invariants for links in $S3$ shown by M. Eisermann. We next present a 2-cocycle so that the associated invariant is equivalent to the signature of 4-dimensional manifolds.

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講 演 者: 芦原 聡介(広島大学)
タ イ ト ル: Biquandle presentations of surface links from ch-diagrams

A biquandle is a set with four binary operations which satisfy some axioms corresponding to Reidemeister moves. A surface link is a closed oriented surface embedded in four-space. It is known that a biquandle gives an invariant for a surface link and any surface link is presented by a link diagram with some markers which is called a ch-diagram. The speaker gives a method that we directly calculate the biquandle of a surface link from a ch-diagram presenting the surface.

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講 演 者: 小谷 賀子(奈良女子大学)
タ イ ト ル: A new bridge index for links with trivial knot components

In 1954, H. Schubert introduced the concept of bridge indices for knots. For satellite knots, he gave an estimation of bridge indices by using index of the pattern and the bridge index of the companion of the satellite knot under consideration. In 2003, J.Schultens gave a modern proof of the result by using foliation.

In this talk, we consider bridge indices of links. We introduce a new bridge index for non-split 2-component links such that one component of each link is a trivial knot. Roughly speaking, the bridge index is the minimum of the bridge numbers of a link under the constraint that one component of the link is in a minimal bridge position. We give an estimation of the bridge index for satellite links by using the technique of Schultens'. We show, by using the estimation, the new bridge index is essentially different from the standard one.

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講 演 者: 田中 亮吉 (京都大学)
タ イ ト ル: Penner-Andersen's Fatgraph Models of Proteins

In 2009, R.C.Penner and J.E.Andersen proposed to classify conformations of proteins by using topological invariants. They introduced the Fatgraph for modeling proteins and constructed an algorithm to calculate those invariants. Their methods are suitable for computation and existing database implies that their invariants could be useful for structural classification of proteins. I would like to introduce their methods and also propose some questions.

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講 演 者: 金信 泰造 (大阪市立大学)
タ イ ト ル: Band surgery on 2-component links

An oriented 2-component link is called band-trivializable, if it can be unknotted by a single band surgery. We consider whether a given 2-component link is band-trivializable or not. Then we can completely determine the band-trivializability for the prime links with up to 9 crossings. We use the signature, the Jones and Q polynomials, and the Arf invariant. Since a band-trivializable link has 4-ball genus zero, we also give a table for the 4-ball genus of the prime links with up to 9 crossings. Furthermore, we give an additional answer to the problem of whether a $(2n+1)$-crossing 2-bridge knot is related to a $(2,2n)$ torus link or not by a band surgery for $n=3$, $4$, which was brought from the study of a DNA site-specific recombination.

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講 演 者: 屋代 司 (Sultan Qaboos University)
タ イ ト ル: Cell-complexes for surface diagrams and Roseman moves

A surface-knot is a connected oriented closed surface embedded in 4-space. If we project a surface-knot in 3-space, then we obtain a surface diagram that may have double points or triple points or branch points. The preimage of the set of multiple points is the union of two families of connected components called the upper and lower double decker set. The lower decker set induces a cell-complex for the surface diagram. There is a set of local deformations of the cell-complex induced from Roseman moves. In this talk we discuss about a relation between these local moves and cell-complexes.

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講 演 者: 今別府 孝規 (広島大学)
タ イ ト ル: On normalized arrow polynomials of checkerboard colorable virtual links

It is known that every classical knot diagram is checkerboard colorable, but every virtual knot diagram is not checkerboard colorable. Normalized arrow polynomials introduced by Kauffman are a generalization of Jones polynomials. We show that some virtual links are not checkerboard colorable by using a certain property of normalized arrow polynomials.

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講 演 者: 栗屋 隆仁(大阪市立大学数学研究所(OCAMI))
タ イ ト ル: Mosaic quantum knots and related topics

In a recent work of Samuel J. Lomonaco Jr and Louis H. Kauffman, they consider the concept of mosaic quantum knots in the context of quantum graphs. We review mosaic knot theory and introduce related topics and our recent results.

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講 演 者: 早野 健太(大阪大学)
タ イ ト ル: Classification of genus-1 simplified broken Lefschetz

Broken Lefschetz fibrations were introduced as a generalization of Lefschetz fibrations to near-symplectic setting. In this talk, we first construct a family of genus-1 simplified broken Lefschetz fibrations. We then show that all genus-1 simplified broken Lefschetz fibrations with small number of Lefschetz singularities are contained in the family we construct.

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講 演 者: 張 娟姫 (広島大学)
タ イ ト ル: Bridge presentations of links and Heegaard splittings of 3-manifolds

It is known that bridge presentations of links in the 3-sphere are deeply related with Heegaard splittings of 3-manifolds. The speaker has used this relation and studied Heegaard splittings of certain 3-manifolds to obtain several results on bridge presentations of links. In this talk, we give a brief survey on the results and show you how to use the relation.

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講 演 者: 田山 育男 (大阪市立大学数学研究所(OCAMI))
タ イ ト ル: Enumerating 3-manifolds with the first homology groups
isomorphic to (Z/nZ)+(Z/nZ) with lengths up to 10

This is a joint work with A. Kawauchi. A well-order was introduced on the set of links by A. Kawauchi. This well-order also naturally induces a well-order on the set of prime link exteriors and eventually induces a well-order on the set of closed connected orientable $3$-manifolds. With respect to this order, we enumerated the prime links and the prime link exteriors with lengths up to 10. In this talk, we show a list of the enumeration of $3-$manifolds with the first homology groups isomorphic to (Z/nZ)+(Z/nZ) with lengths up to 10 by using the enumeration of the prime link exteriors.

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講 演 者: 伊藤 哲也 (東京大学)
タ イ ト ル: Links having non-left orderable 2-fold branched coverings

The (left) orderability of 3-manifold groups is closely related to the existence of certain foliations or laminations. Recently, it is observed that the left-orderbility is also related to Heegaard Floer homologies. Thus it is interesting to construct examples of 3-manifolds having non- left orderable fundamental group. In this talk I will give a family of links whose 2-fold branched covering has non-left orderable fundamental group.

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講 演 者: 清水 理佳 (大阪市立大学数学研究所(OCAMI))
タ イ ト ル: Region crossing change is an unknotting operation

K. Kishimoto proposed a new local transformation on a knot or link diagram called a region crossing change. In this talk, we show that a region crossing change on a knot diagram is an unknotting operation, and we define the region unknotting numbers for a knot diagram and a knot.

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最終更新日: 2012年1月30日
(C)大阪市大数学教室