The evenness conjecture in equivariant unitary bordism

TL;DR

This paper reviews the evenness conjecture in equivariant unitary bordism, discussing known cases and properties that enable proofs, contributing to understanding the structure of these bordism groups.

Contribution

It summarizes existing results and identifies key properties that allow proving the evenness conjecture in specific cases.

Findings

The conjecture holds in certain known cases.

Properties enabling proof are highlighted.

The paper clarifies the structure of equivariant unitary bordism groups.

Abstract

The evenness conjecture for the equivariant unitary bordism groups states that these bordism groups are free modules over the unitary bordism ring on even-dimensional generators. In this paper we review the cases in which the conjecture is known to hold and we highlight the properties that permit one to prove the conjecture in these cases.