On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions

Details On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions

2003-12-03

arxiv.org/abs/math/0312085v1

Mathematics

Symplectic Geometry

15 pages

Scientific paper

Let $(M, \omega)$ be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian $S^1$ action such that the fixed point set consists of isolated points or surfaces. Assume dim $H^2(M)<3$, in \cite{L}, we defined a certain invariant of such spaces which consists of fixed point data and twist type, and we divided the possible values of these invariants into six ``types''. In this paper, we construct such manifolds with these ``types''. As a consequence, we have a precise list of the values of these invariants.

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