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

Details 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

2004-10-18

arxiv.org/abs/math/0410398v1

Mathematics

Algebraic Topology

19 pages, uses pictex

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-399460