Comparing globular complex and flow

Details Comparing globular complex and flow Comparing globular complex and flow

2003-08-07

arxiv.org/abs/math/0308063v3

New-York Journal of Mathematics, vol. 11 : p. 97-150, 2005

Mathematics

Algebraic Topology

54 pages ; 3 figures ; Second paper corresponding to the content of math.AT/0201252 ; v2 : very minor changes ; v3 : final ver

Scientific paper

A functor is constructed from the category of globular CW-complexes to that of flows. It allows the comparison of the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, it is proved that this functor induces an equivalence of categories from the localization of the category of globular CW-complexes with respect to S-homotopy equivalences to the localization of the category of flows with respect to weak S-homotopy equivalences. As an application, we construct the underlying homotopy type of a flow.

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