Cohomology algebra of the orbit space of free circle group actions on lens spaces

Details Cohomology algebra of the orbit space of free circle group actions on lens spaces Cohomology algebra of the orbit space of free circle group actions on lens spaces

2008-06-11

arxiv.org/abs/0806.1814v1

Mathematics

Algebraic Topology

12 Pages

Scientific paper

Suppose that G=S^1 acts freely on a finitistic space X whose mod p cohomology ring isomorphic to that of a lens space L^{2m-1}(p;q_1,...,q_m). In this paper, we determine the mod p cohomology ring of the orbit space X/G. If the characteristic class \alpha\belongs H^2(X/G;Z_p) of the S^1-bundle S--> X--> X/G is nonzero, then mod p ndex of the action is deined to be the largest integer n such that \alpha^n is nonzero. We also show that the mod p index of a free action of S^1 on a lens space L^(2m-1)(p;q_1,...,q_m) is p-1, provided that \alpha is nonzero.

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