Cohomology algebra of the orbit space of free circle group actions on lens spaces
نویسنده
چکیده
Suppose that G = S acts freely on a finitistic space X whose mod p cohomology ring isomorphic to that of a lens space L(p; q1, . . . , qm). In this paper, we determine the mod p cohomology ring of the orbit space X/G. If the characteristic class α ǫH(X/G;Zp) of the S -bundle S →֒ X → X/G is nonzero, then the mod p index of the action is defined to be the largest integer n such that α 6= 0. We also show that the mod p index of a free action of S on a lens space L(p; q1, . . . , qm) is p− 1, provided that α 6= 0.
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