A C-symplectic free 𝑆¹-manifold with contractible orbits and 𝐂𝐀𝐓=\frac12𝐃𝐈𝐌

Allday, Christopher; Oprea, John

doi:10.1090/S0002-9939-05-07945-1

A C-symplectic free $S^1$-manifold with contractible orbits and $\mathbf {CAT} = \frac 12\mathbf {DIM}$
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Proc. Amer. Math. Soc. 134 (2006), 599-604 Request permission

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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