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Mathematics > Algebraic Topology

arXiv:math/0702677 (math)
[Submitted on 22 Feb 2007]

Title:A new higher homotopy groupoid: the fundamental globular omega-groupoid of a filtered space

Authors:Ronald Brown
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Abstract: We use the n-globe with its skeletal filtration to define the fundamental globular omega--groupoid of a filtered space; the proofs use an analogous fundamental cubical omega--groupoid due to the author and Philip Higgins. 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 omega-groupoid on one element of dimension n is the fundamental crossed complex of the n-globe.
Comments: 18 pages. 2 eps files
Subjects: Algebraic Topology (math.AT); Category Theory (math.CT)
MSC classes: 18D10, 18G30, 18G50, 20L05, 55N10, 55N25
Cite as: arXiv:math/0702677 [math.AT]
  (or arXiv:math/0702677v1 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.math/0702677
Journal reference: Homotopy, Homology and Applications, 10 (2008), No. 1, pp.327-343

Submission history

From: Ronald Brown [view email]
[v1] Thu, 22 Feb 2007 21:57:53 UTC (40 KB)
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