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 globular!–groupoid. The proofs use an analogous fundamental cubical!–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!-groupoid on one element of dimensionn is the fundamental crossed complex of then-globe.