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(2015年度)
2014年度
2015年度組織委員 安部 哲哉 ・ 岡崎 真也

 数学教室は2014年12月に理学部に移転しました.
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理学部「12」の建物です.
(F棟は学術情報総合センターに近い方です)
講 演 者 :新國 亮 (東京女子大学)
タ イ ト ル :On calculations of the twisted Alexander ideals for spatial graphs,
handlebody-knots and surface-links
(アブストラクト) (PDF)
日 時 :5月1日(金)16:00~17:00
場 所 :大阪市立大学理学部 中講究室(理学部 F棟 415号室)
Toptop
講 演 者 :松崎 尚作 (早稲田大学)
タ イ ト ル :Arrangements of links on surfaces arranged in $\mathbb{R}^3$
(アブストラクト) (PDF)
日 時 :4月24日(金)16:00~17:00
場 所 :大阪市立大学理学部 中講究室(理学部 F棟 415号室)
Toptop
講 演 者 :滝岡 英雄 (OCAMI)
タ イ ト ル :A characterization of the $\Gamma$-polynomials of knots with the clasp numbers at most two
(アブストラクト) (PDF)
日 時 :4月17日(金)16:00~17:00
場 所 :大阪市立大学理学部 中講究室(理学部 F棟 415号室)
Toptop
講 演 者 :安部 哲哉 (OCAMI)
タ イ ト ル :Infinitely many ribbon disks with the same exterior
(アブストラクト) (PDF)
日 時 :4月10日(金)16:30~17:30
場 所 :大阪市立大学理学部 中講究室(理学部 F棟 415号室)
Toptop



アブストラクト集



講 演 者: 新國 亮 (東京女子大学)
タ イ ト ル: On calculations of the twisted Alexander ideals for spatial graphs,
handlebody-knots and surface-links

We calculate the twisted Alexander ideals for spatial graphs, handlebody-knots, and surface-links. For spatial graphs, we calculate the invariants of Suzuki's theta-curves and show that the invariants are nontrivial for Suzuki's theta-curves whose Alexander ideals are trivial. For handlebody-knots, we give a remark on abelianizations and calculate the invariant of the handlebody-knots up to six crossings. For surface-links, we correct Yoshikawa's table and calculate the invariants of the surface-links in the table. This is a joint work with Atsushi Ishii (University of Tsukuba) and Kanako Oshiro (Sophia University).

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講 演 者: 松崎 尚作 (早稲田大学)
タ イ ト ル: Arrangements of links on surfaces arranged in $\mathbb{R}^3$

A finite set of two-dimensional manifolds embedded in three-dimensional Euclidean space is called an $\textit{arrangement}$ $\textit{of}$ $\textit{surfaces}$. A link $L$ is said to be $\textit{arrangeable}$ on an arrangement $\mathcal{F}$ of surfaces if there exists a link $L'$ which is ambient isotopic to $L$ such that each component of $L'$ is contained in a surface belonging to $\mathcal{F}$. We consider the following problems. (1) Given an arrangement of surfaces, determine links which can be arrangeable on it. (2) Given a link, determine arrangements of surfaces on which the link is arrangeable. I will talk about partial answers to the problems.

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講 演 者: 滝岡 英雄 (OCAMI)
タ イ ト ル: A characterization of the $\Gamma$-polynomials of knots with the clasp numbers at most two

It is known that every knot bounds a singular disk whose singular set consists of only clasp singularities. Such a singular disk is called a clasp disk. The clasp number of a knot is the minimum number of clasp singularities among all clasp disks of the knot. The $\Gamma$-polynomial is the common zeroth coefficient polynomial of both the HOMFLYPT and Kauffman polynomials. I will talk about a characterization of the $\Gamma$-polynomials of knots with the clasp numbers at most two.

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講 演 者: 安部 哲哉 (OCAMI)
タ イ ト ル: Infinitely many ribbon disks with the same exterior

A classical Gluck's theorem states that there exist at most two inequivalent 2-knots with diffemorphic exteriors. In this talk, we construct infinitely many ribbon disks with the same exterior. First, we give a sufficient condition for a given slice disk to be ribbon. Next, we construct infinitely many slice disks with the same exterior, and prove that these are ribbon. This is a joint work with Motoo Tange. If time permits, we prove that these ribbon disks are mutually distinct by the (overtwisted) contact structures in the 3-sphere.

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最終更新日: 2015年4月8日
(C)大阪市大数学教室