Name  Teruaki Kitano 

Affiliation  Soka University 
Talk type  Session 
Time  Jan 10 13:00~13:40 
Location  E11103 
Title  On the Alexander polynomial of a knot as an obstruction for SL(2,Z/n)representations of a knot group 
Abstract 
Let $K$ be a knot in $S^3$ and $G(K)$ its knot group. It is known that the special value of the Alexander polynomial of $K$ at an integer $n$ gives an obstruction for the existence of representations of $G(K)$ into the symmetric group of some degree. In this talk I review this classical theory first. Secondly we mention the existence of $SL(2,Z/n)$representations of $G(K)$ with the nontrivial Alexander polynomial for infinitely many $n$, as an application.

Slide  103110/east8_v0109.pdf 