Concordance homomorphisms from knot Floer homology
Peter Ozsvath, Andras Stipsicz, Zoltan Szabo

TL;DR
This paper introduces a new family of knot invariants derived from knot Floer homology that serve as homomorphisms from the smooth concordance group to integers, providing bounds on knot genera.
Contribution
It develops a modified construction of knot Floer homology to produce a one-parameter family of concordance homomorphisms with applications to knot genus bounds.
Findings
Provides bounds on the four-ball genus of knots.
Establishes homomorphisms from the concordance group to integers.
Demonstrates applications to knot theory problems.
Abstract
We modify the construction of knot Floer homology to produce a one-parameter family of homologies for knots in the three-sphere. These invariants can be used to give homomorphisms from the smooth concordance group to the integers, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.
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