Semi-free Hamiltonian circle actions on 6 dimensional symplectic manifolds

Details Semi-free Hamiltonian circle actions on 6 dimensional symplectic manifolds Semi-free Hamiltonian circle actions on 6 dimensional symplectic manifolds

2002-10-28

arxiv.org/abs/math/0210431v1

Mathematics

Symplectic Geometry

27pages,13 figures

Scientific paper

Assume $(M, \omega)$ is a connected, compact 6 dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action, such that the fixed point set consists of isolated points or compact orientable surfaces. We restrict attention to the case $\dim$ $H^2(M)<3$. We give a complete list of the possible manifolds, determine their equivariant cohomology ring and equivariant Chern classes. Some of these manifolds are classified up to diffeomorphism. We also show the existence for a few cases.

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