Equivariant complex bundles, fixed points and equivariant unitary bordism

TL;DR

This paper investigates fixed points of universal G-equivariant complex vector bundles, providing a decomposition formula that advances understanding of equivariant K-theory and bordism groups for subgroup families.

Contribution

It introduces a new decomposition formula for fixed points of universal G-equivariant bundles, linking to equivariant K-theory and bordism groups.

Findings

Decomposition formula for fixed points of universal G-equivariant bundles.

Description of fixed points in equivariant K-theory spectrum.

Analysis of equivariant unitary bordism groups for subgroup families.

Abstract

We study the fixed points of the universal G-equivariant n-dimensional complex vector bundle and obtain a decomposition formula in terms of twisted equivariant universal complex vector bundles of smaller dimension. We use this decomposition to describe the fixed points of the complex equivariant K-theory spectrum and the equivariant unitary bordism groups for adjacent families of subgroups.