The Alexander polynomial

Geometry Topology Student Seminar
Wednesday, October 4, 2017 - 13:55
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech
Let K be a tame knot in S^3.  Then the Alexander polynomial is knot invariant, which consists of a Laurent polynomial arising from the infinite cyclic cover of the knot complement.  We will discuss the construction of the Alexander polynomial and, more generally, the Alexander invariant from a Seifert form on the knot.  In addition, we will see some connections between the Alexander polynomial and other knot invariants, such as the genus and crossing number.