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Title:
The generalization of the Goldman bracket to Three dimensions and its relation to Geometrization
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Abstract:
This lecture begins with some background to the joint work of Moira Chas and Siddartha Gadgil recognizing "geometrization". We describe elementary pictorial computations of the zeroth, first and second homology of the space of unparametrized generic closed curves in a compact three manifold.The degree one piece has a pictorial lie algebra structure which acts as a lie algebra on each piece.This structure is part of "String Topology". arXiv:math/9911159v1 . See also wikipedia String Topology.
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