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Nontoric Hamiltonian circle actions on four-dimensional symplectic orbifolds
Author(s):
S.
F.
Singer;
J.
Talvacchia;
N.
Watson
Journal:
Proc. Amer. Math. Soc.
127
(1999),
937-940.
MSC (1991):
Primary 58Fxx
MathSciNet review:
1487340
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References |
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Abstract:
We construct four-dimensional symplectic orbifolds admitting
Hamiltonian circle actions with isolated fixed points, but not admitting any Hamiltonian action of a two-torus. One example is linear, and one example is compact.
References:
- [AH]
- Ahara, K. and A. Hattori, 4 dimensional symplectic
 -manifolds admitting moment map, J. Fac. Sci. Univ. Tokyo Sect. IA, Math. 38 (1991), 251-298. MR 93b:58048 - [At]
- Atiyah, M. F., Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15. MR 83e:53037
- [Au]
- Audin, M., Hamiltoniens périodiques sur les variétés symplectiques compactes de dimension 4, Géometrie symplectique et méchanique, Proceedings 1988, C. Albert ed., Springer Lecture Notes in Math. 1416 (1990). MR 91f:57013
- [GS]
- Guillemin, V. and S. Sternberg, Convexity properties of the moment mapping I, Invent. Math. 67 (1982), 491-513. MR 83m:58037
- [K]
- Karshon, Y., Periodic Hamiltonian flows on four-dimensional manifolds, Trans. AMS, submitted. (Available electronically at dg-ga/9510004.)
- [LT]
- Lerman, E. and S. Tolman, Hamiltonian torus actions on symplectic orbifolds and toric varieties, Trans. AMS. 349 (1997), 4201-4230. (Available electronically at dg-ga/9511008.) MR 98a:57043
- [T]
- Tolman, S., Examples of Non-Kaehler Hamiltonian Torus Actions, Invent. Math., to appear.
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Additional Information:
S.
F.
Singer
Affiliation:
Department of Mathematics, Haverford College, Haverford, Pennsylvania 19041
Email:
ssinger@haverford.edu
J.
Talvacchia
Affiliation:
Department of Mathematics, Swarthmore College, Swarthmore, Pennsylvania 19081
Email:
jtalvac1@swarthmore.edu
N.
Watson
Affiliation:
Department of Mathematics, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104
DOI:
10.1090/S0002-9939-99-04767-X
PII:
S 0002-9939(99)04767-X
Received by editor(s):
July 8, 1997
Additional Notes:
The second author was supported in part by a fellowship from the American Association of University Women and NSF grant DMS 9304580.
Communicated by:
Peter Li
Copyright of article:
Copyright
1999,
American Mathematical Society
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