Involuções fixando FnUF3

Abstract

Let Mm a closed and smooth m-dimensional manifold and T : Mm - Mm a smooth involution defined on Mm. It is well known that the fixed point set F of T is a finite and disjoint union of closed submanifolds, with possibly different dimensions. Write F = [n i=0Fi, n _ m, where Fi denotes the union of those components of dimension i. Suppose that F has the form Fn [ Fj , 0 _ j < n, and that F does not bound. From the Five Halves Theorem of J. Boardman, one then has m _ 5 2 n. In this work, our interest is to obtain improvements of this general bound in the case F = Fn [ F3, where n > 3. Results of this nature were obtained by R. E. Stong and P. Pergher for j = 0, S. Kelton for j = 1 and F. Figueira for j = 2. We will see that a general bound in this case is m(n-3)+6, where m(n) is a number discovered by Stong and Pergher which works as a best possible bound for the case F = Fn [ fptog (j = 0).