Negative amphicheiral knots provide torsion elements in the knot concordance group, and torsion elements are less understood than infinite-order elements. In this talk, I will introduce an equivariant version of the Alexander polynomial (called the half-Alexander polynomial) for strongly negative amphicheiral knots, focusing on its applications to knot concordance. In particular, we will show how understanding the geography behavior of the half-Alexander polynomial led to the construction of the first examples of non-slice amphichiral knots of determinant 1. This talk is based on joint work with Keegan Boyle.
Location: MATH 204