Virtual Morse theory on ΩHam(M, ϖ)

Yakov Savelyev University of Massachusetts

Differential Geometry mathscidoc:1609.10167

Journal of Differential Geometry, 84, (2), 409-425, 2010
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[5].
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  title={Virtual Morse theory on ΩHam(M, ϖ) },
  author={Yakov Savelyev},
  booktitle={Journal of Differential Geometry},
Yakov Savelyev. Virtual Morse theory on ΩHam(M, ϖ) . 2010. Vol. 84. In Journal of Differential Geometry. pp.409-425.
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