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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Eduardo Gonzalez
Journal: Trans. Amer. Math. Soc. 358 (2006), 2927-2948
MSC (2000): Primary 53D05, 53D45
Published electronically: March 1, 2006
MathSciNet review: 2216253
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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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Additional Information

Eduardo Gonzalez
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11777
Address at time of publication: Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854
Email: eduardo@math.sunysb.edu, eduardog@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04038-4
PII: S 0002-9947(06)04038-4
Keywords: Symplectic manifold, Hamiltonian $S^{1}$ action, quantum cohomology, Seidel element
Received by editor(s): April 2, 2004
Published electronically: March 1, 2006
Additional Notes: This work was partially supported by CONACyT-119141
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.