TRANSFORMATION GROUPS ON HOMOLOGICAL MANIFOLDS

Abstract

Abstract : Let G be a topological transformation group on a compact Hausdorff space Y and F(G;Y) its fixed point set. The analysis is devoted to the study of the cohomology structure of F(G;Y) in the following three cases: (1) G is the group Z2 of integers modulo 2 an Y has the mod 2 cohomology ring of the real projective n-space. (2) G is the group Zp of integers modulo p, where p is an odd prime number, and Y has the mod P cohomology structure of the lense ( <N+1)- space mod p. (3) G is the circle group S' and Y has the integral cohomology ring of the complex projective n-space. For simplicity, we shall call Y a cohomology real projective n-space or a cohomology lense (<N+1)-space mod p or a cohomology complex projective n-space if its cohomology structure is that described in (1 OR (2) or (3).