|Time||Jan 10 13:00~13:40|
|Title||On the Alexander polynomial of a knot as an obstruction for SL(2,Z/n)-representations of a knot group|
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 non-trivial Alexander polynomial for infinitely many $n$, as an application.