Geodesic
A new higher homotopy groupoid: the fundamental globular $ω$-groupoid of a filtered space
Homology, homotopy, and applications, Tome 10 (2008) no. 1, pp. 327-343.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2008.v10.n1.a14
Classification : 18D10, 18G30, 18G50, 20L05, 55N10, 55N25
Keywords: filtered space, higher homotopy groupoid, higher homotopy van Kampen theorem, cubical singular complex, free globular groupoid 
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     author = {Ronald Brown},
     title = {A new higher homotopy groupoid: the fundamental globular $\ensuremath{\omega}$-groupoid of a filtered space},
     journal = {Homology, homotopy, and applications},
     pages = {327--343},
     publisher = {mathdoc},
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     number = {1},
     year = {2008},
     doi = {10.4310/HHA.2008.v10.n1.a14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n1.a14/}
}
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Ronald Brown. A new higher homotopy groupoid: the fundamental globular $ω$-groupoid of a filtered space. Homology, homotopy, and applications, Tome 10 (2008) no. 1, pp. 327-343. doi : 10.4310/HHA.2008.v10.n1.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n1.a14/

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