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On the homology of semi-direct products of groups
by
José Andrés Armario
Dpto. Matematica Aplicada I, Univ. de Sevilla
Coauthors: Victor Alvarez, Pedro Real
We here deal with the problem of calculating the homology of a semi-direct product G ×j G' of groups, being the factors G and G' finitely generated abelian groups. A first step in order to design an algorithm for computing this homology is the obtention of a simplicial isomorphism between the classifying space [`W](G ×j G') and a twisted cartesian product [`W](G) ×\tau [`W](G'). Taking as data the homological information on the factors given in terms of contractions (special homotopy equivalences) and using jointly Brown's theorem and the homological perturbation machinery, we get an explicit contraction from the normalized chain complex associated to [`W](G ×j G') to a free DG-module of finite type. This last complex is a ``twisted'' tensor product in the fashion of Prouté.
Date received: May 14, 1998
Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabc-14.