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|Abstract:||Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A(F) and to a three-manifold Y with boundary identified with F a module over A (F). In this paper, we establish naturality properties of this invariant. Changing the diffeomorphism between F and the boundary of Y tensors the bordered invariant with a suitable bimodule over A (F). These bimodules give an action of a suitably based mapping class group on the category of modules over A (F). The Hochschild homology of such a bimodule is identified with the knot Floer homology of the associated open book decomposition. In the course of establishing these results, we also calculate the homology of A (F). We also prove a duality theorem relating the two versions of the 3-manifold invariant. Finally, in the case of a genus-one surface, we calculate the mapping class group action explicitly. This completes the description of bordered Heegaard Floer homology for knot complements in terms of the knot Floer homology.|
|Electronic Publication Date:||10-Apr-2015|
|Citation:||Lipshitz, Robert, Ozsvath, Peter S, Thurston, Dylan P. (2015). Bimodules in bordered Heegaard Floer homology. GEOMETRY & TOPOLOGY, 19 (525 - 724. doi:10.2140/gt.2015.19.525|
|Pages:||525 - 724|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||GEOMETRY & TOPOLOGY|
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