Cohomology obstructions to certain circle actions

Details Cohomology obstructions to certain circle actions Cohomology obstructions to certain circle actions

2011-04-04

arxiv.org/abs/1104.0452v1

Mathematics

Algebraic Topology

9 pages

Scientific paper

Given a closed oriented manifold $M^{2n}$ and $c\in H^2(M)$, we shall investigate the relations between the non-vanishing of $(c^n)\cdot[M]$ and lower bounds of the fixed points of circle actions on $M$. We first review some known results, due to Hattori, Fang-Rong and Pelayo-Tolman respectively, then unify and generalize these results into a new theorem. The main ingredients of the proof are a result of lifting circle actions to complex line bundles, due to Hattori and Yoshida, and an $S^1$-equivariant localization formula, largely due to Bott. Some remarks and related results are also discussed.

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