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

R. Brown·H. K. Kamps·T. Porter
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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.

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BibTeXRIS

R. Brown, H. K. Kamps, T. Porter. 2004-10-18. A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem. https://arxiv.org/abs/math/0410398

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