Friday Seminar on Knot Theory(2016年度)

組織委員 安部 哲哉・岡崎 真也

日時 2017年2月10日(金)16:00~17:30
場所 理学部 F棟 415号室(中講究室)
講演者(所属) 16:00~16:30
Celeste Damiani(Osaka City University, JSPS)
タイトル The many faces of Loop Braid Groups
アブストラクト Loop braid groups, are a generalization of braid groups. These groups have been an object of interest in different domains of mathematics and mathematical physics, and have been called, in addition to loop braid groups, with several names such as of motion groups, groups of permutation-conjugacy automorphisms, braid-permutation groups, welded braid groups and untwisted ring groups. We unify all the formulations that have appeared so far in the literature, with a complete proof of the equivalence of these definitions. We also introduce an extension of these groups that appears to be a more natural generalization of braid groups from the topological point of view.
講演者(所属) 16:30~17:00
Jieon Kim (Osaka City University, JSPS)
タイトル Marked graph diagrams of immersed surface-links
アブストラクト An immersed surface-link is the image of the disjoint union of oriented surfaces in the 4-space $\mathbb R^4$ by a smooth immersion. By using normal forms of immersed surface-links defined by S. Kamada and K. Kawamura, we define marked graph diagrams of immersed surface-links. In addition, we generalize Yoshikawa moves for marked graph diagrams of surface-links to local moves for marked graph diagrams of immersed surface-links. We give some examples of marked graph diagrams of immersed surface-links. This is a joint work with S. Kamada, A. Kawauchi and S. Lee.
講演者(所属) 17:00~17:30
María de los Angeles Guevara Hernández(Instituto Potosino de
Investigacion Cientifica y Tecnologica, and Osaka City University)
タイトル Infinite families of prime knots with alternation number $1$ and
dealternating number $n$.
アブストラクト The alternation number of a knot $K$, denoted by $alt(K)$, is the minimum number of crossing changes necessary to transform a diagram of $K$ into some (possibly non-alternating) diagram of an alternating knot. And the dealternating number of a knot $K$, denoted by $dalt(K)$, is the minimum number of crossing changes necessary to transform a diagram $D$ of $K$ into an alternating diagram. So, from these definitions it is immediate that $alt(K) \leq dalt(K)$ for any knot $K$. In this talk, we will show that for each positive integer $n$ there exists a family of infinitely many hyperbolic prime knots with alternation number 1 and dealternating number $n$.
日時 2017年1月27日(金)16:00~17:00
講演者(所属) 石井 敦 (筑波大学)
タイトル On augmented Alexander matrices
場所 理学部 F棟 415号室(中講究室)
アブストラクト We introduce augmented Alexander matrices, and construct link invariants. An augmented Alexander matrix is defined with an Alexander triple, which gives an extension of a quandle. This framework gives the twisted Alexander invariant and the quandle cocycle invariant. This is a joint work with Kanako Oshiro.
日時 2017年1月13日(金)16:00~17:00
講演者(所属) 阪田 直樹 (広島大学)
タイトル Veering triangulations of mapping tori of some pseudo-Anosov maps arising from Penner's construction
場所 理学部 F棟 415号室(中講究室)
アブストラクト Agol proved that every pseudo-Anosov mapping torus of a surface, punctured along the singular points of the stable and unstable foliations, admits a canonical "veering" ideal triangulation. In this talk, I will describe the veering triangulations of the mapping tori of some pseudo-Anosov maps arising from Penner's construction.
日時 12月9日(金)16:00~17:00
講演者(所属) 浮田卓也(東京工業大学)
タイトル Planar Lefschetz fibrations and Stein structures with distinct Ozsvath-Szabo invariants on corks
場所 理学部 F棟 415号室(中講究室)
アブストラクト Thanks to a result of Lisca and Matic and a refinement by Plamenevskaya, it is known that on a 4-manifold with boundary Stein structures with non-isomorphic $Spin^c$ structures induce contact structures with distinct Ozsvath-Szabo invariants. Here we give an infinite family of examples showing that converse of Lisca-Matic-Plamenevskaya theorem does not hold in general. Our examples arise from Mazur type corks.
日時 12月2日(金)16:00~17:00
講演者(所属) 佐藤進(神戸大学)
タイトル The ribbon stable class of a surface-link
場所 理学部 F棟 415号室(中講究室)
アブストラクト Two orientable surface-links are called stably equivalent if they are ambient isotopic in $4$-space up to adding or deleting trivial $1$-handles. In this talk, we construct a map $\omega$ from the set of orientable surface-links to that of stable equivalence classes of ribbon surface-links, and study several properties of $\omega$. In particular, we prove that $\omega(F)=[F]$ for any ribbon surface-link $F$, that $F$ and $\omega(F)$ have the same fundamental quandle, that $\omega(F)$ has a representative of genus $1$ for any deform-spinning of a $2$-bridge knot, and that $\omega(\tau^0 L)=\omega(\tau^1 L)$ for any link $L$, where $\tau^k L$ is the $k$-turned spinning of $L$.
日時 11月18日(金)16:00~17:00
講演者(所属) 野坂武史 (九州大学 数理学研究院)
タイトル Milnor invariants via unipotent Magnus embeddings
場所 理学部 F棟 415号室(中講究室)
アブストラクト We reconfigure Milnor invariant, in terms of central group extensions and unipotent Magnus embeddings, and develop a diagrammatic computation of the invariant. In this talk, we explain the reconfiguration and the computation with mentioning some examples. This is a joint work with Hisatoshi Kodani.
日時 11月4日(金)16:00~17:00
講演者(所属) 伊藤哲也(大阪大学)
タイトル Bi-ordering and Alexander invariants
場所 理学部 F棟 415号室(中講究室)
アブストラクト We show that if a knot group (more generally, finitely presented group) is bi-orderable then its Alexander polynomial has at least one positive real root.
日時 10月28日(金)16:00~17:00
講演者(所属) 石川勝巳(京都大学数理解析研究所)
タイトル On the classification of smooth quandles
場所 理学部 F棟 415号室(中講究室)
アブストラクト A smooth quandle is a differentiable manifold with a smooth quandle operation. We show that every smooth transitive connected quandle is isomorphic to a homogeneous space with an operation defined from a group automorphism. We also give an explicit classification of such quandles of dimension 1 and 2.
日時 10月21日(金)15:00~16:00
講演者(所属) 大森 源城 (東京工業大学)
タイトル A small normal generating set for the handlebody subgroup of the Torelli group
場所 理学部 F棟 415号室(中講究室)
アブストラクト We consider the handlebody subgroup of the Torelli group, i.e. the intersection of the handlebody group and the Torelli group of an orientable surface. The handlebody subgroup of the Torelli group is related to integral homology 3-spheres through the Heegaard splittings. In this talk, we give a small normal generating set for the handlebody subgroup of the Torelli group.
日時 7月22日(金)16:00~17:00
講演者(所属) 門上 晃久 (金沢大学)
タイトル Three amphicheiralities of a virtual link
場所 理学部 F棟 415号室(中講究室)
アブストラクト We define three amphicheiralities for a virtual link by using its geometric realization.
日時 7月15日(金)16:00~17:00
講演者(所属) 野崎 雄太 (東京大学)
タイトル An explicit relation between knot groups in lens spaces and those in $S^3$
場所 理学部 F棟 415号室(中講究室)
アブストラクト We consider a $p$-fold cyclic covering map $(S^3, K) \to (L(p,q), K')$ and describe the knot group $\pi_1(S^3 \setminus K)$ in terms of $\pi_1(L(p,q) \setminus K')$. As a consequence, we give an alternative proof for the fact that a certain knot in $S^3$ cannot be represented as the preimage of any knot in a lens space. In the proof, the subgroup of a group $G$ generated by the commutators and the $p$th power of each element of $G$ plays a key role.
日時 6月24日(金)16:00~17:00
講演者(所属) 屋代司(Suntan Qaboos University, Oman)
タイトル Pseudo-cycles of surface-knots and their applications
場所 理学部 F棟 415号室(中講究室)
アブストラクト A surface-knot is a closed oriented surface smoothly embedded in 4-space. A surface-knot diagram of a surface-knot is the projected image in 3-space under the orthogonal projection with crossing information. The pre-image of multiple point sets of a surface-knot diagram is called a double decker set that is the union of lower and upper decker sets. The lower decker set induces a complex consisting of rectangular cells. In this talk we define pseudo-cycles in the complex. We prove that for a fixed quandle, the maximal number of pseudo-cycles for all colourings is an invariant under Roseman moves up to the quandle homology. As its application, we discuss about the triple point number of some surface-knots.
日時 6月17日(金)16:00~17:00
講演者(所属) 村上広樹 (東京工業大学)
タイトル Alternating links and root polytopes
場所 理学部 F棟 415号室(中講究室)
アブストラクト In this talk, a relationship between the determinant of an alternating link and a certain polytope obtained from the link diagram is presented. Concretely, we show that the volume of the obtained polytope is proportional to the determinant if the given link is alternating.
日時 5月27日(金)16:00~17:00
講演者(所属) 和田 康載(早稲田大学)
タイトル Milnor invariants of covering links
場所 理学部 F棟 415号室(中講究室)
アブストラクト We consider Milnor invariants for certain covering links as a generalization of covering linkage invariants formulated by R. Hartley and K. Murasugi. A set of Milnor invariants for covering links is a cobordism invariant of a link, and that this invariant can distinguish some links for which the ordinary Milnor invariants coincide.Moreover, for a Brunnian link $L$, the first non-vanishing Milnor invariants of $L$ is modulo-$2$ congruent to a sum of Milnor invariants of covering links. As a consequence, a sum of linking numbers of "iterated" covering links gives the first non-vanishing Milnor invariant of $L$ modulo $2$. This talk is a joint work with Natsuka Kobayashi and Akira Yasuhara.
日時 5月13日(金)16:00~17:00
講演者(所属) Sang Youl Lee (Pusan National University)
タイトル The quantum $A_2$ polynomial for oriented virtual links
場所 理学部 F棟 415号室(中講究室)
アブストラクト A tangled trivalent graph diagram is an oriented link diagram possibly with some trivalent vertices whose incident edges are oriented all inward or all outward. Two tangled trivalent graph diagrams are said to be regular isotopic if they are transformed into each other by a finite sequence of classical Reidemeister moves of type 2, type 3 and trivalent vertex passing moves. In 1994, G. Kuperberg derived an inductive, combinatorial definition of a polynomial-valued regular isotopy invariant (called the quantum $A_2$ invariant) of links and tangled trivalent graph diagrams with values in the integral Laurent polynomial ring $\mathbb Z[a, a^{-1}]$ that equals the Reshetikhin-Turaev invariant corresponding to the simple Lie algebra $A_2$. In this talk, I would like to talk about an extension of the quantum $A_2$ invariant to virtual tangled trivalent graph diagrams and a derived polynomial invariant for oriented virtual links satisfying a certain skein relation.
日時 4月8日(金)16:00~17:00
講演者(所属) 河内明夫(OCAMI)
タイトル On a cross-section of an immersed sphere-link in 4-space
場所 理学部 F棟 415号室(中講究室)
アブストラクト The torsion Alexander polynomial, the reduced torsion Alexander polynomial and the local signature invariant of a cross-section of an immersed sphere-link are investigated from the viewpoint of how to influence to the immersed sphere-link. It is shown that the torsion Alexander polynomial of a symmetric middle cross-section of a ribbon sphere-link is an invariant of the ribbon sphere-link. A generalization to a symmetric middle cross-section of an immersed ribbon sphere-link is given.
最終更新日: 2017年2月7日
管理者: 安部哲哉 tabe(at)sci.osaka-cu.ac.jp