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Quantum cohomology and  -actions with isolated fixed points
Author(s):
Eduardo
Gonzalez
Journal:
Trans. Amer. Math. Soc.
358
(2006),
2927-2948.
MSC (2000):
Primary 53D05, 53D45
Posted:
March 1, 2006
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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  -dimensional manifold of this type is isomorphic to the (small) quantum cohomology of a product of  copies of  . This generalizes a result due to Tolman and Weitsman.
References:
-
- 1.
- D. Austin and P. Braam, Morse-Bott theory and equivariant cohomology, in The Floer Memorial Volume, Progress in Mathematics 133, Birkhäuser (1995). MR 1362827 (96i:57037)
- 2.
- A. Hattori, Symplectic manifolds with semifree Hamiltonian
 actions, Tokyo J. Math. 15 (1992), 281-296. MR 1197098 (93m:57043) - 3.
- F. C. Kirwan, Cohomology of quotients in Symplectic and Algebraic Geometry. Mathematical Notes 31. Princeton University Press (1984). MR 0766741 (86i:58050)
- 4.
- D. McDuff and S. Tolman, Topological properties of Hamiltonian circle actions, preprint available at arXiv.math.SG/0404338.
- 5.
- D. McDuff and D. Salamon, Introduction to Symplectic Topology, 2nd edition, Oxford Univ. Press, New York (1998) MR 1698616 (2000g:53098)
- 6.
- D. McDuff and D. Salamon, J-Holomorphic Curves and Symplectic Topology, AMS Colloquium Publications, 52, Amer. Math. Soc. (2004). MR 2045629 (2004m:53154)
- 7.
- M. Schwarz, Equivalences for Morse homology, in Geometry and Topology in Dynamics (ed. M. Barge, K. Kuperberg), Contemporary Mathematics 246, Amer. Math. Soc. (1999), 197-216. MR 1732382 (2000j:57070)
- 8.
- M. Schwarz, Morse Homology, Birkäuser Verlag (1999). MR 1239174 (95a:58022)
- 9.
- P. Seidel,
 of symplectic automorphism groups and invertibles in quantum cohomology rings, Geom. and Funct. Anal. 7 (1997), 1046 -1095. MR 1487754 (99b:57068) - 10.
- S. Tolman and J. Weitsman, On semifree symplectic circle actions with isolated fixed points, Topology 39 (2000), 299-309. MR 1722020 (2000k:53074)
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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:
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
Posted:
March 1, 2006
Additional Notes:
This work was partially supported by CONACyT-119141
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Guangcun Lu, Symplectic capacities of toric manifolds and related results, http://arxiv.org/abs/math/0312483, posted on 05/03/2006 (electronic).
Dusa McDuff and Susan Tolman, Topological Properties of Hamiltonian Circle Actions, International Mathematics Research Papers Volume 2006 (2006), 1–77 .
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