A bigroupoid's topology (or, Topologising the homotopy bigroupoid of a space)
arXiv:1302.7019 · doi:10.1007/s40062-016-0160-0
Abstract
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.
arXiv commentV1 26 pages, 8 figures. Preliminary version, comments welcome; V2 25 pages, 5 figures. HHA style, submitted for publication. License is CC-BY, V3 18 pages, final version to appear in JHRS. License is CC0