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.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 1, pp.327-343.
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