15 February 2009 Hamiltonian S1-manifolds are uniruled
Dusa Mcduff
Author Affiliations +
Duke Math. J. 146(3): 449-507 (15 February 2009). DOI: 10.1215/00127094-2009-003

Abstract

The main result of this article is that every closed Hamiltonian S1-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 π1 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 [15, Th. 5.15]. 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

Citation

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Dusa Mcduff. "Hamiltonian S1-manifolds are uniruled." Duke Math. J. 146 (3) 449 - 507, 15 February 2009. https://doi.org/10.1215/00127094-2009-003

Information

Published: 15 February 2009
First available in Project Euclid: 14 January 2009

zbMATH: 1183.53080
MathSciNet: MR2484280
Digital Object Identifier: 10.1215/00127094-2009-003

Subjects:
Primary: 14E08 , 53D05 , 53D45

Rights: Copyright © 2009 Duke University Press

Vol.146 • No. 3 • 15 February 2009
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