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Bordered Heegaard Floer Homology

Memoirs of the American Mathematical Society

Genres: Geometry, Topology
Format: Paperback / softback
Publisher: American Mathematical Society, Providence, United States
Published: 30th Jul 2018
Dimensions: w 178mm h 254mm d 20mm
Weight: 523g
ISBN-10: 1470428881
ISBN-13: 9781470428884
Barcode No: 9781470428884
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Synopsis
The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type $D$) is a module over the algebra and the other of which (type $A$) is an $\mathcal A_\infty$ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the $\mathcal A_\infty$ tensor product of the type $D$ module of one piece and the type $A$ module from the other piece is $\widehat{HF}$ of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for $\widehat{HF}$. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

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