# Friday Seminar on Knot Theory（2016年度）

 組織委員　安部 哲哉・岡崎 真也

 今後の講演
 日時 ： 4月8日（金）16：00～17：00 講演者 ： 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)

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.

 日時 ： 5月13日（金）16：00～17：00 講演者 ： 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)

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 ： 5月27日（金）16：00～17：00 講演者 ： 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)

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 ： 6月17日（金）16：00～17：00 講演者 ： 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)

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.

 最終更新日: 2016年4月8日 管理者: 安部哲哉 tabe(at)sci.osaka-cu.ac.jp