October 15, 2007
Michael Usher (Princeton): Spectral numbers in Floer theories
Abstract:
In Floer homology theories, one can associate to any Floer homology
class its spectral number, defined as the infimum of the action-levels
of chains representing that homology class. In the case of Hamiltonian
Floer homology, these spectral numbers have been studied by Oh and
Schwarz and play a role in the recent work of Entov and Polterovich.
I'll sketch a proof that the infimum in the definition of the spectral
number is always attained (even when the set of critical values of the
action functional is dense in R). This fact allows some of the
applications of the spectral numbers that have been carried out for
special classes (e.g., rational or semipositive) closed symplectic
manifolds to be generalized to all closed symplectic manifolds.
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