1 research outputs found
One-connectivity and finiteness of Hamiltonian -manifolds with minimal fixed sets
Let the circle act effectively in a Hamiltonian fashion on a compact
symplectic manifold . Assume that the fixed point set
has exactly two components, and , and that . We first show that , and are simply connected. Then we
show that, up to -equivariant diffeomorphism, there are finitely many such
manifolds in each dimension. Moreover, we show that in low dimensions, the
manifold is unique in a certain category. We use techniques from both areas of
symplectic geometry and geometric topology