A homotopy double groupoid of a Hausdorff space II: A van Kampen  Theorem

A homotopy double groupoid of a Hausdorff space II: A van Kampen Theorem (2005)

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by R. Brown , K. H. Kamps , T. Porter

Venue:	THEORY AND APPLICATIONS OF CATEGORIES
Citations:	15 - 10 self

BibTeX

@MISC{Brown05ahomotopy,
    author = {R. Brown and K. H. Kamps and T. Porter},
    title = {A homotopy double groupoid of a Hausdorff space II: A van Kampen Theorem},
    year = {2005}
}

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Abstract

This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a suitable tool for nonabelian, 2-dimensional, local-to-global problems. The methods are analogous to those developed by Brown and Higgins for similar theorems for other higher homotopy groupoids. An integral part of the proof is a detailed discussion of commutative cubes in a double category with connections, and a proof of the key result that any composition of commutative cubes is commutative. These results have recently been generalised to all dimensions by Philip Higgins.

Citations

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1	The classifying spce of a crossed complex - Brown, Higgins - 1991