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


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.)


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.


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

2010 Mathematics Subject Classification

18E15, 55Q91, 57R18

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