Computing Crossed Modules Induced by an Inclusion of a Normal Subgroup, with Applications to Homotopy 2-types
نویسندگان
چکیده
We obtain some explicit calculations of crossedQ-modules induced from a crossed module over a normal subgroup P of Q. By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2-types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups. Introduction A crossed module M = (μ : M → P ) has a classifying space BM (see, for example, [4]) which is of the homotopy type of B(P/M) if μ is the inclusion of the normal subgroup M of P . Consider a homotopy pushout X of the form
منابع مشابه
Computing Crossed Modules Induced by an Inclusion of a Normal Subgroup with Applications to Homotopy Types
We obtain some explicit calculations of crossed Q modules induced from a crossed module over a normal subgroup P of Q By virtue of theorems of Brown and Higgins this enables the computation of the homotopy types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups Introduction A crossed module M M P has a classifying space BM see for example ...
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We obtain some explicit calculations of crossed Q-modules induced from a crossed module over a normal subgroup P of Q. By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2-types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups.
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