Quantum cohomology and $S^1$-actions with isolated fixed points

Details Quantum cohomology and $S^1$-actions with isolated fixed points Quantum cohomology and $S^1$-actions with isolated fixed points

2003-10-08

arxiv.org/abs/math/0310114v1

Mathematics

Symplectic Geometry

20 pages

Scientific paper

This paper studies symplectic manifolds that admit semi-free circle actions with isolated fixed points. We prove, using results on the Seidel element due to McDuff and Tolman, that the (small) quantum cohomology of a $2n$ dimensional manifold of this type is isomorphic to the (small) quantum cohomology of a product of $n$ copies of $\bb{P}^1$. This generalizes a result due to Tolman and Witsman.

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