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Periodic Hamiltonian Flows on Four Dimensional Manifolds
Yael Karshon, Hebrew University of Jerusalem, Israel
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Memoirs of the American Mathematical Society
1999; 71 pp; softcover
Volume: 141
ISBN-10: 0-8218-1181-9
ISBN-13: 978-0-8218-1181-8
List Price: US$45
Individual Members: US$27
Institutional Members: US$36
Order Code: MEMO/141/672
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Abstract. We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian \(S^1\)-spaces. Additionally, we show that all these spaces are Kähler, that every such space is obtained from a simple model by a sequence of symplectic blowups, and that if the fixed points are isolated then the space is a toric variety.

Readership

Graduate students and research mathematicians interested in global analysis, analysis on manifolds, and symplectic geometry.

Table of Contents

  • Introduction
  • Graphs
  • Metrics
  • Uniqueness: Graph determines space
  • Isolated fixed points implies toric variety
  • Blowing-up
  • Completing the classification; our spaces are Kähler
  • Appendices
  • References
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