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Whitehead Torsion for Floer HomologyGeometry/Topology
|Speaker: ||Michael Sullivan, Stanford University|
|Location: ||693 Kerr|
|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.