Journal of Homotopy and Related Structures

, Volume 11, Issue 4, pp 923–942 | Cite as

A bigroupoid’s topology (or, Topologising the homotopy bigroupoid of a space)

  • David Michael Roberts


The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroupoid internal to the category of topological spaces, as Brown and Danesh-Naruie lifted the fundamental groupoid to a topological groupoid. For locally relatively contractible spaces the resulting topological bigroupoid is locally trivial in a way analogous to the case of the topologised fundamental groupoid. This is the published version of arXiv:1302.7019.


Fundamental bigroupoid Homotopy 2-type Topological bigroupoid 

Mathematics Subject Classification

18D05 22A22 55Q05 



Thanks are due to several anonymous referees who helped beat this article into shape over several iterations, and to Tim Porter for both inviting its submission to this volume and his subsequent patience. Thanks also to Ronnie Brown, whose lovely book on groupoids [4] and topology was influential in my thesis work (of which this paper formed a small part) in ways that are not apparent to the casual observer: Happy Birthday Ronnie!


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Copyright information

© Tbilisi Centre for Mathematical Sciences 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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