# Heegaard Floer homology for tangles and cobordisms between them

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Akram Alishahi , Columbia University
Fine Hall 314

Heegaard Floer homology was generalized for non-closed 3-manifolds with certain boundary decoration called sutured manifolds, by Juhasz, Eftekhary and I. Sutured manifolds can be described as a generalization of oriented tangles. We use this description to define a notion of cobordism between sutured manifolds. Associated with cobordisms between sutured manifolds we will describe the definition of 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.