Equivariant factorization homology of global quotient orbifolds

TL;DR

This paper develops equivariant factorization homology for manifolds with finite group actions, extending existing frameworks and providing new tools for invariants and applications in representation theory.

Contribution

It introduces equivariant factorization homology, extending the axiomatic framework to include multiplicative invariants under group actions, and establishes its key properties.

Findings

Equivariant factorization homology satisfies an equivariant tensor excision property.

Examples include Bredon equivariant homology and twisted Hochschild homology.

Applications include constructions of categorical braid group actions.

Abstract

We introduce equivariant factorization homology, extending the axiomatic framework of Ayala-Francis to encompass multiplicative invariants of manifolds equipped with finite group actions. Examples of such equivariant factorization homology theories include Bredon equivariant homology and (twisted versions of) Hochschild homology. Our main result is that equivariant factorization homology satisfies an equivariant version of tensor excision, and is uniquely characterised by this property. We also discuss applications to representation theory, such as constructions of categorical braid group actions.