Twisted Bredon-Illman Cohomology is a Morita Invariant

TL;DR

This paper proves that twisted Bredon-Illman cohomology for compact Lie group action groupoids remains invariant under Morita equivalence, extending previous results by removing key restrictions.

Contribution

It demonstrates Morita invariance of twisted Bredon-Illman cohomology for a broader class of groupoids, generalizing earlier work by eliminating finite isotropy and coefficient system restrictions.

Findings

Morita invariance of twisted Bredon-Illman cohomology established

Generalizes previous results by removing finite isotropy restrictions

Uses bibundles to transfer coefficient systems between groupoids

Abstract

We show that the twisted Bredon-Illman cohomology defined by Mukherjee-Mukherjee applied to compact Lie group action groupoids is Morita-invariant. This cohomology uses coefficient systems twisted over the discrete tom Dieck equivariant fundamental groupoid. To show Morita invariance, we use bibundles to transfer coefficient systems from one groupoid to another Morita equivalent one. This generalises results of Pronk-Scull on ordinary Bredon-Illman cohomology by removing both the finite isotropy condition and restrictions on the coefficient systems.