Homology, Homotopy and Applications

Volume 23 (2021)

Number 1

The equivariant fundamental groupoid as an orbifold invariant

Pages: 25 – 47

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n1.a3

Authors

Dorette Pronk (Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada)

Laura Scull (Department of Mathematics, Fort Lewis College, Durango, Colorado, U.S.A.)

Abstract

We construct a $2$-category version of Tom Dieck’s equivariant fundamental groupoid for representable orbifolds and show that the discrete fundamental groupoid is Morita invariant; hence it is an orbifold invariant for representable orbifolds.

Keywords

equivariant homotopy theory, orbifold, fundamental groupoid, groupoid, Morita invariance

2010 Mathematics Subject Classification

18E15, 55Q91, 57R18

Full Text (PDF format)

The first author’s research is funded by an NSERC Discovery Grant.

Received 4 October 2019

Received revised 18 February 2020

Accepted 4 March 2020

Published 5 August 2020