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Friday, February 26, 2016
3:00 PM - 5:00 PM

Geometry and Topology Seminar

Heegaard Floer homology for tangles and cobordisms between them
Akram Alishahi, Ritt Assistant Professor, Mathematics, Columbia University,
An extention of the hat Heegaard Floer homology for 3-manifolds with boundary (together with an extra structure over the boundary), called sutured manifolds, was defined by Juhasz. We introduce a framework that generalizes Juhasz's construction and brings different flavors of Heegaard Floer homology for closed 3-manifolds, knots and links under the same roof. Sutured manifolds can be described as a generalization of oriented tangles. We use this description to introduce a notion of cobordism between sutured manifolds, and associated with these cobordisms we define an invariant homomorphism between Heegaard Floer homologies of the corresponding sutured manifolds. These maps generalize cobordism maps associated to 4-dimensional cobordisms between closed 3-manifolds and define cobordism maps for decorated cobordisms between pointed knots. This is a joint work with Eaman Eftekhary. 



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