Homology, Homotopy and Applications
Volume 10 (2008)
A new higher homotopy groupoid: the fundamental globular $ω$-groupoid of a filtered space
Pages: 327 – 343
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.
filtered space, higher homotopy groupoid, higher homotopy van Kampen theorem, cubical singular complex, free globular groupoid
2010 Mathematics Subject Classification
18D10, 18G30, 18G50, 20L05, 55N10, 55N25