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午後３時００分〜４時００分　長郷 文和 氏（東工大 学振特別研究員）
題目：Algebraic varieties via a deformation of the Kauffman bracket skein module

講演概要

Algebraic varieties via a deformation of the Kauffman bracket skein module
長郷 文和（東工大 学振特別研究員）

In this talk, we will introduce an algebraic variety in an affine space $�mathbb{C}^N$ constructed via the Kauffman bracket skein module (KBSM) of a knot exterior. One of the main ideas for the construction of the variety is that the polynomial map from $�mathbb{C}^N$ to itself can be defined by using a representation of the braid group into the endomorphisms of the KBSM of a handlebody. In fact, the algebraic variety turns out to be an invariant of knots in $S^3$. In this talk, we will try to get a better understanding of the variety by focusing on the number of its irreducible components. Then we will see a relationship of the variety with so-called the Casson-Lin invariant defined by X-.S-. Lin, which in fact inspired the above main idea, and moreover a relationship of the variety with the highest degree of the A-polynomial $A_K(M,L)$ in terms of $L$.

Party 代数の構造と既約表現
小須田 雅（琉球大理学部）

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