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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A C-symplectic free $S^1$-manifold with contractible orbits and $\mathbf{CAT} = \frac12\,\mathbf{DIM}$

Authors: Christopher Allday and John Oprea
Journal: Proc. Amer. Math. Soc. 134 (2006), 599-604
MSC (2000): Primary 57E25; Secondary 55C30, 53D05
Published electronically: June 29, 2005
MathSciNet review: 2176029
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Abstract: An interesting question in symplectic geometry concerns whether or not a closed symplectic manifold can have a free symplectic circle action with orbits contractible in the manifold. Here we present a c-symplectic example, thus showing that the problem is truly geometric as opposed to topological. Furthermore, we see that our example is the only known example of a c-symplectic manifold having non-trivial fundamental group and Lusternik-Schnirelmann category precisely half its dimension.

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Additional Information

Christopher Allday
Affiliation: Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, Hawaii 96822-2273

John Oprea
Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115

PII: S 0002-9939(05)07945-1
Received by editor(s): June 20, 2004
Received by editor(s) in revised form: September 16, 2004
Published electronically: June 29, 2005
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.