Open Access
February 2010 Virtual Morse theory on ΩHam(M, ϖ)
Yakov Savelyev
J. Differential Geom. 84(2): 409-425 (February 2010). DOI: 10.4310/jdg/1274707319


We relate previously defined quantum characteristic classes to Morse theoretic aspects of the Hofer length functional on Ham (M, ω). As an application we prove a theorem which can be interpreted as stating that this functional is “virtually” a perfect Morse-Bott functional. This can be applied to study the topology and Hofer geometry of Ham(M, ω). We also use this to give a prediction for the index of some geodesics for this functional, which was recently partially verified by Yael Karshon and Jennifer Slimowitz.


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Yakov Savelyev. "Virtual Morse theory on ΩHam(M, ϖ)." J. Differential Geom. 84 (2) 409 - 425, February 2010.


Published: February 2010
First available in Project Euclid: 24 May 2010

zbMATH: 1196.53052
MathSciNet: MR2652467
Digital Object Identifier: 10.4310/jdg/1274707319

Rights: Copyright © 2010 Lehigh University

Vol.84 • No. 2 • February 2010
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