Computing HF^ by factoring mapping classes

Abstract

Bordered Heegaard Floer homology is an invariant for three-manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F a differential graded algebra, and to an arc slide between two handle decompositions, a bimodule over the two algebras. In this paper, we describe these bimodules for arc slides explicitly, and then use them to give a combinatorial description of HF^ of a closed three-manifold, as well as the bordered Floer homology of any 3-manifold with boundary.

106 pages, 46 figures

References in corpus (5)

• Floer homology and knot complements
• Bimodules in bordered Heegaard Floer homology
• Bordered Floer homology for sutured manifolds
• Heegaard Floer homology as morphism spaces
• Combinatorial Heegaard Floer homology and nice Heegaard diagrams

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• Combinatorial Proofs in Bordered Heegaard Floer homology
• Holomorphic polygons and the bordered Heegaard Floer homology of link complements
• Bordered Floer Homology and Lefschetz fibrations with corners
• Bordered Floer Homology of (2,2n)-Torus Link Complement
• Relative Q-gradings from bordered Floer theory