Abstract
1. Equivariant cohomology. Let A be a space with a continuous fixed point free involution a: A --A. Consider the two possible actions of a on the coefficient group Z of integers: the trivial action and the nontrivial one. Let I9+(A) (resp. H7+(A)) denote the equivariant (resp. residual) ith cohomology group of A for the trivial action; and let HL (A) (resp. m (A)) denote the corresponding equivariant (resp. residual) cohomology groups for the nontrivial action of a on Z (the singular homology is considered throughout; see [1]). The groups 0 i ~~~0 H+ (A) and Hi (A) can also be described as the corresponding cohomology groups of the orbit space A/a, with the constant and twisted coefficients { Z}, respectively. There are exact sequences:
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