On the obstructed Lagrangian Floer theory
Algebraic Structures in the Theory of Holomorphic Curves
November 19, 2009 11:00 AM to 12:00 PM
Speakers:
Cho, Cheol-Hyun
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Abstract: |
Lagrangian Floer homology in a general case has been constructed by
Fukaya, Oh, Ohta and Ono, where they construct an A-infinity algebra
or an A-infinity bimodule from Lagrangian submanifolds, and studied
the obstructions and deformation theories. But for obstructed
Lagrangian submanifolds, standard Lagrangian Floer homology can not be
defined.
We explore several well-known cohomology theories on these A-infinity
objects and explore their properties, which are well-defined and
invariant even in the obstructed cases. These are Hochschild and
cyclic homology of an A-infinity objects and Chevalley-Eilenberg or
cyclic Chevalley-Eilenberg homology of their underlying L-infinity
objects. We provide some computations and also explain their
relationships to the cluster homology theory of Lagrangian
submanifolds by Cornea and Lalonde |
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