A new higher homotopy groupoid: The fundamental globular ω-groupoid of a filtered space

Abstract

We show that the graded set of filter homotopy classes rel vertices of maps from the n-globe to a filtered space may be given the structure of (strict) globular ω-groupoid. The proofs use an analogous fundamental cubical ω-groupoid due to the author and Philip Higgins in 1981. 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 ω-groupoid on one element of dimension n is the fundamental crossed complex of the n-globe. Copyright © 2008, Ronald Brown.