Involuções fixando espaços projetivos.

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

Suppose M is a smooth, closed manifold and T : M ! M is a smooth involution defined on M. It is well known that the fixed point set F of T is a finite and disjoint union of closed submanifolds of M. For a given F, a basic problem in this context is the classification, up to equivariant cobordism, of the pairs (T;M) for which the fixed point set is F. For F = RP(n), the classification was established by P. E. Conner, E. E. Floyd and R. E. Stong. D. C. Royster then studied this problem with F the disjoint union of two real projective spaces, F = RP(m) [ RP(n). He established the results via a case-by-case method depending on the parity of m and n, with special arguments when one of the components is RP(0) = fpointg, but his methods were not sucient to handle the case when m and n are even and positive. The first objective of this work is to obtain the complex and quaternionic versions of the results obtained by Conner, Floyd, Stong and Royster, which means to replace the division ring R by the division rings C (complex numbers) and H (quaternionic numbers); in other words, to replace each involved RP(n) by either CP(n) or HP(n). Concerning the question left open by Royster recently some particular cases were considered; specifically, the case m = n = even >0, established by D. Hou and B. Torrence, and the case m = 2 and n = 2q, where q >1 is odd, established by R. de Oliveira. The second and more important goal of this work is to attack other cases of the Royster question. In this direction, we completely solve the particular case F = RP(2s) [ RP(2n), with s; n 1. We also solve the question of finding the maximal codimension with respect to which F = RP(m)[RP(n), with 0 m

ASSUNTO(S)

classes características topologia algebrica bordismo topologia algébrica fibrados vetoriais involuções

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