Agradecimentos

Abstract

In this work is studied the rank of the fixed point set of a semifree action on spaces X ∼ p S n × S n and X ∼ p S n × S n × S n , with n > 0. We also consider the extension of the result for actions of p -groups on spaces X ∼ p S n × S m , with 0 < n ≤ m . As result of the techniques used, we give a description of the differential d 1 of a spectral sequence that converges to Tate equivariant cohomology, as well a version of the K¨unneth Formule to Tate equivariant cohomology. At the end, motivated by the space form problem for infinite groups we compute the cohomology of the virtually cyclic groups ( Z a (cid:111) Z b ) (cid:111) Z and [ Z a (cid:111) ( Z b × Q 2 1 )] (cid:111) Z .