Actions of groups on sphere product, cohomology of virtually cyclic groups (ZaX| Zb)X| Z and [ZaX|(ZbXQ2i)]X|Z and Tate Cohomology

Neste trabalho inicialmente estudamos o rank da co-homologia do espaço dos pontos fixos de uma \'Z IND.p\' - ação semilivre sobre espaços X~p \' S POT. n\' x \'S POT.n\' e X~p \'S POT.n\' x \'S POT.n\' x \'S POT.n\' , com n>0. Em seguida, estudamos uma extensão para ações de p-grupos sobre espaços X~p \'S POT.n\' X \'S POT.m\', com 00. We also consider the extension of the result for actions of p-groups on spaces X~p \'SPOT.n\' X \' S POT.m\' , with 0<n \'< OR =\' m. As result of the techniques used, we give a description of the differential d1 of a spectral sequence that converges to Tate equivariant cohomology, as well a version of the Künneth 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 IND. a\' X| \'Z IND. b\' )X| Z and [\'Z IND.a\' X|(\'Z IND. b\' X \'Q IND2 POT. i\' )] X|