Bordered Floer Homology and Lefschetz fibrations with corners

Tova Brown

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arXiv · 1310.3446

Bordered Floer Homology and Lefschetz fibrations with corners

Tova Brown

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Abstract

Lipshitz, Ozsváth and Thurston defined a bordered Heegaard Floer invariant CFDA for 3-manifolds with two boundary components, including mapping cylinders for surface diffeomorphisms. We define a related invariant for certain 4-dimensional cobordisms with corners, by associating a morphism F from CFDA(f) to CFDA(g) to each such cobordism between two mapping cylinders f and g. Like the Ozsváth-Szabó invariants of cobordisms between closed 3-manifolds, this morphism arises from counting holomorphic triangles on Heegaard triples. We demonstrate that the homotopy class of the morphism F only depends on the symplectic structure of the cobordism in question.

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Tova Brown. 2013-10-13. Bordered Floer Homology and Lefschetz fibrations with corners. https://arxiv.org/abs/1310.3446

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