Bordered Heegaard Floer homology and graph manifolds

Abstract

We perform two explicit computations of bordered Heegaard Floer invariants. The first is the type D trimodule associated to the trivial S^1 bundle over the pair of pants P. The second is a bimodule that is necessary for self-gluing, when two torus boundary components of a bordered manifold are glued to each other. Using the results of these two computations, we describe an algorithm for computing HF-hat of any graph manifold.

59 pages, 21 figures, new version corrects typos and adds a short discussion of gradings

Cited by in corpus (8)

• L-spaces, taut foliations, and graph manifolds
• Cabling in terms of immersed curves
• Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds
• A calculus for bordered Floer homology
• Peculiar modules for 4-ended tangles
• The Alexander module, Seifert forms, and categorification
• Holomorphic polygons and the bordered Heegaard Floer homology of link complements
• Bordered Floer Homology of (2,2n)-Torus Link Complement