Twisting, mutation and knot Floer homology

  • Peter Lambert-Cole

    Indiana University, Bloomington, USA

Abstract

Let be a knot with a fixed positive crossing and the link obtained by replacing this crossing with positive twists. We prove that the knot Floer homology 'stabilizes' as 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 of positive mutants with isomorphic bigraded groups, Seifert genera, and concordance invariant .

Cite this article

Peter Lambert-Cole, Twisting, mutation and knot Floer homology. Quantum Topol. 9 (2018), no. 4, pp. 749–774

DOI 10.4171/QT/119