A survey on Heegaard Floer homology and concordance
Jennifer Hom
TL;DR
This survey reviews various knot concordance invariants derived from Heegaard Floer homology and establishes a stable equivalence condition for concordant knots based on their Floer complexes.
Contribution
It compiles and discusses multiple invariants from Heegaard Floer homology and proves a new stable equivalence criterion for concordant knots.
Findings
Knot Floer complexes of concordant knots are stably equivalent.
Comprehensive overview of Heegaard Floer invariants in knot concordance.
New theoretical link between knot concordance and Floer homology.
Abstract
In this survey article, we discuss several different knot concordance invariants coming from the Heegaard Floer homology package of Ozsvath and Szabo. Along the way, we prove that if two knots are concordant, then their knot Floer complexes satisfy a certain type of stable equivalence.
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