The equivariant concordance group is not abelian

TL;DR

This paper demonstrates that the equivariant concordance group is non-abelian by providing explicit examples of nontrivial commutators, highlighting its complex algebraic structure.

Contribution

The paper proves the non-abelian nature of the equivariant concordance group through explicit construction of nontrivial commutators.

Findings

Equivariant concordance group is non-abelian

Constructs infinite family of nontrivial commutators

Highlights complex algebraic structure of the group

Abstract

We prove that the equivariant concordance group $\widetilde{\mathcal{C}}$ is not abelian by exhibiting an infinite family of nontrivial commutators.