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Computation and homotopical applications of induced crossed modules. (English) Zbl 1026.55012
Working on the generalization of the fundamental group to higher dimensions, the main structures are crossed modules, particularly through explicit computations. The present paper explains how the computation of induced crossed modules allows the computation of certain homotopy 2-types (like second homotopy groups) and gives many examples and applications.

MSC:
55P15 Classification of homotopy type
18D35 Structured objects in a category (MSC2010)
20J15 Category of groups
55Q99 Homotopy groups
18G55 Nonabelian homotopical algebra (MSC2010)
Software:
Gpd; GAP; XMod
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References:
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