February 7, 2007
Peter Albers (NYU): Floer homology for negative line bundles with applications to Hamiltonian chords
Abstract:
I will report on work in progress with Urs Frauenfelder. We
consider negative line bundles associated to rational symplectic
manifolds. Any Hamiltonian function on the base can be lifted to a
non-compactly supported Hamiltonian function on the total space of
the line bundle. First I will outline how to define Floer homology for
this non-compact situation and give some non-trivial invariance
statements. Furthermore, to a given Lagrangian submanifold a
corresponding version of Floer homology can be defined. The isomorphism
types of these homologies depend strongly on the negativity of the line
bundle. In both situations there is a fascinating interplay between
periodic orbits resp. Hamiltonian chords on the total space and the
base. As an application we establish the existence of infinitely
geometrically distinct quantized chords on symplectically aspherical Lagrangian submanifolds.
back to the seminar homepage