Bordered Floer homology for sutured manifolds

By Rumen Zarev. 2009

56 citations recorded by the source corpus.

We define a sutured cobordism category of surfaces with boundary and 3-manifolds with corners. In this category a sutured 3-manifold is regarded as a morphism from the empty surface to itself. In the process we define a new class of geometric objects, called bordered sutured manifolds, that generalize both sutured 3-manifolds and bordered 3-manifolds. We extend the definition of bordered Floer homology to these objects, giving a functor from a decorated version of the sutured category to A-infinity algebras, and A-infinity bimodules. As an application we give a way to recover the sutured homology SFH(Y,Gamma) of a sutured manifold from either of the bordered invariants CFA(Y) and CFD(Y) of its underlying manifold Y. A further application is a new proof of the surface decomposition formula of Juhasz.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b6ed82f0d38d88b0fd2f47f9fe4f441cae90409b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Heegaard Floer homology as morphism spaces (2010, background): “The duality results for modules and bimodules can be seen as special cases of results for bordered sutured manifolds [22].”