Memoirs of the American Mathematical Society 1999; 71 pp; softcover Volume: 141 ISBN10: 0821811819 ISBN13: 9780821811818 List Price: US$48 Individual Members: US$28.80 Institutional Members: US$38.40 Order Code: MEMO/141/672
 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
 Blowingup
 Completing the classification; our spaces are Kähler
 Appendices
 References
