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Bangor University - School of Computer Science

Mathematics Preprints 2007

Algebraic Topology

07.05 : BROWN, R.

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

Summary:

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.

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Homology, Homotopy and Applications 10 (2008) 327-343.

07.22 : BROWN, R.

Possible connections between whiskered categories and groupoids, many object Lie algebras, automorphism structures and local-to-global questions

Summary:

We define the notion of whiskered categories and groupoids and discuss potential applications, relations betweens topics, extensions, for example to a many object Lie theory, to automorphism structures for crossed modules, and to resolutions of monoids.
This paper is more an outline of a possible programme or programmes and their relationships than giving conclusive results.

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