$\pi_1$ of Hamiltonian $S^1$ manifolds

Hui Li

$\pi_1$ of Hamiltonian $S^1$ manifolds

Symplectic Geometry 2007-05-23 v2 Algebraic Topology

Authors: Hui Li

Abstract

Let $(M, \omega)$ be a connected, compact symplectic manifold equipped with a Hamiltonian $S^1$ action. We prove that, as fundamental groups of topological spaces, $\pi_1(M)=\pi_1(\hbox{minimum})=\pi_1(\hbox{maximum})=\pi_1(M_{red})$ , where $M_{red}$ is the symplectic quotient at any value in the image of the moment map $\phi$ .

Keywords

symplectic manifold hamiltonian s1 action fundamental group moment map symplectic quotient

Cite

@article{arxiv.math/0203075,
  title  = {$\pi_1$ of Hamiltonian $S^1$ manifolds},
  author = {Hui Li},
  journal= {arXiv preprint arXiv:math/0203075},
  year   = {2007}
}

Comments

4 pages

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