Open Access𝜋₁ of Hamiltonian 𝑆¹ manifolds
Author(s) -
Hui Li
Publication year - 2003
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-03-06881-3
Subject(s) - parenthesis , algorithm , artificial intelligence , computer science , mathematics , philosophy , linguistics
Let ( M , ω ) (M, \omega ) be a connected, compact symplectic manifold equipped with a Hamiltonian S 1 S^1 action. We prove that, as fundamental groups of topological spaces, π 1 ( M ) = π 1 ( m i n i m u m ) = π 1 ( m a x i m u m ) = π 1 ( M r e d ) \pi _1(M)=\pi _1(\mathrm {minimum})=\pi _1(\mathrm {maximum})=\pi _1(M_{red}) , where M r e d M_{red} is the symplectic quotient at any value in the image of the moment map ϕ \phi .