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Virtual Morse theory on \(\Omega \)Ham\((M, \omega)\). (English) Zbl 1196.53052

The author relates the known quantum characteristic classes to Morse theoretic aspects of the Hofer length functional on \(\Omega \,\text{Hom}(M, \omega)\). He also includes a proof of a theorem which states that the Hofer length functional is “virtually” a perfect Morse-Bott functional. This result is used to give a prediction for the index of some geodesics for this functional which was partially verified by Karshon and Slimowitz.

MSC:

53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
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