Trivial tangles, compressible surfaces and Floer homology

Trivial tangles, compressible surfaces and Floer homology

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Akram Alishahi, Columbia University
Fine Hall 314

Heegaard Floer homology has different extensions for 3-manifolds with boundary. In this talk, we will explain how they can be used to give a computationally effective way for detecting boundary parallel components of tangles, and existence of homologically essential compressing disks. The fact that these are checkable by computer, is based on the factoring algorithm of Lipshitz-Ozsvath-Thurston for computing bordered Floer homology, and our extension of it to compute bordered-sutured Floer homology. This is a joint work with Robert Lipshitz.