Quantum cohomology and 𝑆¹-actions with isolated fixed points

Gonzalez, Eduardo

doi:10.1090/S0002-9947-06-04038-4

Quantum cohomology and $S^1$-actions with isolated fixed points
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Trans. Amer. Math. Soc. 358 (2006), 2927-2948 Request permission

Abstract:

This paper studies symplectic manifolds that admit semi-free circle actions with isolated fixed points. We prove, using results on the Seidel element, 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 $\mathbb {P}^1$. This generalizes a result due to Tolman and Weitsman.

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