Homology, Homotopy and Applications

Volume 10 (2008)

Number 1

A new higher homotopy groupoid: the fundamental globular $ω$-groupoid of a filtered space

Pages: 327 – 343

DOI: http://dx.doi.org/10.4310/HHA.2008.v10.n1.a14

Author

Ronald Brown (School of Computer Science, University of Wales, Gwynedd, Wales, United Kingdom)

Abstract

We show that the graded set of filter homotopy classes rel vertices of maps from the $n$-globe to a filtered space may be given the structure of (strict) globular $ω$-groupoid. The proofs use an analogous fundamental cubical $ω$-groupoid due to the author and Philip Higgins in 1981. This method also relates the construction to the fundamental crossed complex of a filtered space, and this relation allows the proof that the crossed complex associated to the free globular $ω$-groupoid on one element of dimension n is the fundamental crossed complex of the $n$-globe.

Keywords

filtered space, higher homotopy groupoid, higher homotopy van Kampen theorem, cubical singular complex, free globular groupoid

2010 Mathematics Subject Classification

18D10, 18G30, 18G50, 20L05, 55N10, 55N25

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