On the knot Floer filtration of the concordance group

TL;DR

This paper explores the structure of a filtration on the smooth concordance group derived from knot Floer complexes and the epsilon invariant, revealing that its indexing set includes the natural numbers cross the integers as an ordered subset.

Contribution

It demonstrates that the filtration's indexing set contains the natural numbers cross the integers as an ordered subset, providing new insights into the structure of the concordance group.

Findings

The filtration's indexing set includes the natural numbers cross the integers.

The knot Floer complex and epsilon invariant define a meaningful filtration.

The structure of the concordance group is better understood through this filtration.

Abstract

The knot Floer complex together with the associated concordance invariant epsilon can be used to define a filtration on the smooth concordance group. We show that the indexing set of this filtration contains the natural numbers cross the integers as an ordered subset.