# Mutation and total dimension in knot Heegaard Floer homology

4:00 pm Thursday, September 12, 2013
Allison Moore (Rice)

One particularly powerful invariant of knots in $$S^3$$ is knot Floer homology, $$\widehat{HFK}_m(K, s)$$. When working with $$\mathbb{Z}/2\mathbb{Z}$$ coefficients, this invariant takes the form of a bigraded vector space, with the total dimension given by the sum over all bigradings of the dimensions of these vector spaces. This sum is conjecturally invariant under Conway mutation, or more generally, genus two mutation. We will construct infinitely many examples of genus two mutant pairs of knots with invariant total dimension and discuss some interesting questions that arise from considering this conjectured invariance. Parts of this work are joint with Starkston and Lidman.