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Whitehead Torsion for Floer HomologyGeometry/Topology
|Speaker:||Michael Sullivan, Stanford University|
|Start time:||Wed, Jan 6 1999, 4:10PM|
Floer homology has become a popular field of study in symplectic geometry, with applications to topics like Lagrangian intersection theory and the Arnold Conjecture. In this lecture I construct two K-theoretic invariants for the chain complexes of Floer homology. First I briefly review the Floer homology theory of two intersecting Lagrangian submanifolds. Then I review algebraic definitions of Whitehead torsion and the second Whitehead group. I show how these algebraic structures can define invariants for a Floer chain complex or one-parameter family of complexes when the Floer homology vanishes. Finally, I sketch a proof which uses 'gluing' theorems and other Floer homology analysis to show that these invariants are independent of almost-complex structures and exact symplectomorphisms.