A. Pereira do Vale & M. R. Pinto (ed.),
Proceedings of the 1st International Meeting on Geometry and Topology.
Proceedings of the conference held in Braga, September 11-13, 1997.
Universidade do Minho, Portugal

On the computability of the $p$-local homology of twisted Cartesian products of Eilenberg-MacLane space

V. Alvarez, J. A. Armario and P. Real

Facultad de Informatica y Estadistica, Avda. Reina Mercedes S.N. 41012, Sevilla, Spain valvarez@euler.fie.us.es

Escuela Universitaria de Ingenieria Tecnica Agricola, Ctra. Utrera Km. 1, 41013, Sevilla, Spain armario@cica.es

Dpto. de Matematica Aplicada I, Universidad de Sevilla, Spain real@cica.es

Abstract: Working in the framework of the Simplicial Topology, a method for calculating the $p$-local homology of a twisted cartesian product $X(\pi,m,\tau, \pi',n) = K(\pi,m)\times_{\tau} K(\pi',n)$ of Eilenberg-Mac Lane spaces is given. The chief technique is the construction of an explicit homotopy equivalence between the normalized chain complex of $X$ and a free DGA-module of finite type $M$, via homological perturbation. If $X$ is a commutative simplicial group (being its inner product the natural one of the cartesian product of $K(\pi,m)$ and $K(\pi',n)$), then $M$ is a DGA-algebra. Finally, in the special case $K(\pi,1) \hookrightarrow X \stackrel{p}{\ra} K(\pi',n)$, we prove that $M$ can be a small twisted tensor product.

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