The Stable Concordance Genus

TL;DR

This paper introduces the stable concordance genus, an invariant that examines how the concordance genus of a knot behaves under connected sum, providing insights into knot theory and concordance classes.

Contribution

The paper defines and explores the stable concordance genus, a new concept extending the understanding of concordance genus in knot theory.

Findings

Defines the stable concordance genus

Analyzes its properties and behavior under connected sum

Highlights its significance in distinguishing knot invariants

Abstract

The concordance genus of a knot is the least genus of any knot in its concordance class. Although difficult to compute, it is a useful invariant that highlights the distinction between the three-genus and four-genus. In this paper we define and discuss the stable concordance genus of a knot, which describes the behavior of the concordance genus under connected sum.