Twisting, mutation and knot Floer homology

2016/08/05 by Lambert-Cole, Peter
#57M27 #57R58 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1608.02011

Abstract

Let L be a knot with a fixed positive crossing and L_n the link obtained by replacing this crossing with n positive twists. We prove that the knot Floer homology \widehatHFK(L_n) `stabilizes' as n goes to infinity. This categorifies a similar stabilization phenomenon of the Alexander polynomial. As an application, we construct an infinite family of prime, positive mutant knots with isomorphic bigraded knot Floer homology groups. Moreover, given any pair of positive mutants, we describe how to derive a corresponding infinite family positive mutants with isomorphic bigraded \widehatHFK groups, Seifert genera, and concordance invariant τ.

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