The knot Floer complex and the smooth concordance group

TL;DR

This paper introduces a new invariant derived from the knot Floer complex to study the smooth concordance group, demonstrating the independence of certain topologically slice knots within it.

Contribution

It defines a novel smooth concordance homomorphism and invariant, providing new tools for analyzing the structure of the smooth concordance group.

Findings

Infinite family of topologically slice knots are independent in the smooth concordance group.

Introduces a new concordance homomorphism based on the knot Floer complex.

Establishes the effectiveness of the epsilon invariant in distinguishing knots.

Abstract

We define a new smooth concordance homomorphism based on the knot Floer complex and an associated concordance invariant, epsilon. As an application, we show that an infinite family of topologically slice knots are independent in the smooth concordance group.