Bordered Floer homology for sutured manifolds

Details Bordered Floer homology for sutured manifolds Bordered Floer homology for sutured manifolds

2009-08-07

arxiv.org/abs/0908.1106v2

Mathematics

Geometric Topology

67 pages, 10 figures. Expanded discussion of gradings. Added graded versions of main results

Scientific paper

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.

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