2 2 Fe b 20 07 A new higher homotopy groupoid : the fundamental globular ω - groupoid of a filtered space ∗

We use the n-globe with its skeletal filtration to define the fundamental globular ω–groupoid of a filtered space; the proofs use an analogous fundamental cubical ω–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 ω-groupoid on one element of dimension n is the fundamental crossed complex of the n-globe.