Genus 2 mutant knots with the same dimension in knot Floer and Khovanov homologies

Details Genus 2 mutant knots with the same dimension in knot Floer and Khovanov homologies Genus 2 mutant knots with the same dimension in knot Floer and Khovanov homologies

2012-04-11

arxiv.org/abs/1204.2524v1

Mathematics

Geometric Topology

14 pages, 8 figures, 3 tables

Scientific paper

We exhibit an infinite family of knots with isomorphic knot Heegaard Floer homology. Each knot in this infinite family admits a nontrivial genus 2 mutant which shares the same total dimension in both knot Floer homology and Khovanov homology. Each knot is distinguished from its genus 2 mutant by both knot Floer homology and Khovanov homology as bigraded groups, as well as by the $\delta$-graded version of knot Heegaard Floer homology.

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