Homology concordance and knot Floer homology

2021/10/27 by Dai, Irving, Hom, Jennifer, Stoffregen, Matthew +1 · 1 citation
#57M25 #57N70 #57R58 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2110.14803

Abstract

We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite number of ℤ-valued, linearly independent homology concordance homomorphisms which vanish for knots coming from S³. This shows that the homology concordance group modulo knots coming from S³ contains an infinite-rank summand. The techniques used here generalize the classification program established in previous papers regarding the local equivalence group of knot Floer complexes over \mathbbF[U, V]/(UV). Our results extend this approach to complexes defined over a broader class of rings.

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• Ribbon knots and iterated cables of fibered knots

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