A calculus for bordered Floer homology

Abstract

We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form, namely, the type D structure may be described graphically by a disjoint union of loops. We develop a calculus for studying bordered invariants of this form and, in particular, provide a complete description of slopes giving rise to L-space Dehn fillings as well as necessary and sufficient conditions for L-spaces resulting from identifying two such manifolds along their boundaries. As an application, we show that Seifert fibered spaces with torus boundary fall into this class, leading to a proof that, among graph manifolds containing a single JSJ torus, the property of being an L-space is equivalent to non-left-orderability of the fundamental group and to the non-existence of a coorientable taut foliation.

79 pages, 14 figures, uses tikz

References in corpus (6)

• Floer Simple Manifolds and L-Space Intervals
• L-spaces, taut foliations, and graph manifolds
• L-space intervals for Graph Manifolds and Cables
• Cabling in terms of immersed curves
• Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds
• The Alexander module, Seifert forms, and categorification

Cited by in corpus (4)

• Floer Simple Manifolds and L-Space Intervals
• Cabling in terms of immersed curves
• L-space intervals for Graph Manifolds and Cables
• Order-detection, representation-detection, and applications to cable knots