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- W2952808265 abstract "The main result of this note is that every closed Hamiltonian S^1 manifold is uniruled, i.e. it has a nonzero Gromov--Witten invariant one of whose constraints is a point. The proof uses the Seidel representation of pi_1 of the Hamiltonian group in the small quantum homology of M as well as the blow up technique recently introduced by Hu, Li and Ruan. It applies more generally to manifolds that have a loop of Hamiltonian symplectomorphisms with a nondegenerate fixed maximum. Some consequences for Hofer geometry are explored. An appendix discusses the structure of the quantum homology ring of uniruled manifolds." @default.
- W2952808265 created "2019-06-27" @default.
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- W2952808265 date "2007-06-05" @default.
- W2952808265 modified "2023-09-27" @default.
- W2952808265 title "Hamiltonian S^1 manifolds are uniruled" @default.
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