Classificação de ações de Z2k fixando espaços projetivos relativos a anéis diferentes

Abstract

Let M be a closed smooth manifold and T : M ! M be an C1 involution defined on M. It is known that if F is the set of fixed points of T, then it is a finite union of closed submanifolds of M. Given F, a problem in this context is the classification, up to equivariant cobordism, of pairs (M; T) for which the fixed point set is F. In this work we performe the classification, up to equivariant cobordism, of Zk 2 -actions (Mn;Φ) fixing F with F being one of the following:

F = KP2n [ KP2m+1; F = KP2n+1 [ KP2m+1

, where KP is the real, complex or quaternionic projective space. We also perform the classification, up to equivariant cobordism, of Z2 2-action whose fixed point set is KdP2n [ K2m+1 e and d < e, where KjP, j = 1; 2; 4 are respectively the real RP, complex CP and quaternionic HP projective spaces. Given that in this case appeared exotic actions, was important that the improvements that we made from the result of Pedro Pergher done in Theorem 3.4.1, which allowed us to obtain such classification.