An absolute Z/2 grading on bordered Heegaard Floer homology

Abstract

Bordered Heegaard Floer homology is an invariant for 3-manifolds, which associates to a surface F an algebra A(F), and to a 3-manifold Y with boundary, together with an orientation-preserving diffeomorphism from F to the boundary of Y, a module over A(F). In a previous paper, we defined relative Z/2 differential gradings on the algebra A(F) and the modules over it. In this paper, we turn the relative grading into an absolute one, and show that the resulting Z/2-graded module is an invariant of the bordered 3-manifold.

24 pages, 3 figures; corrected mistakes and replaced a conjecture with a counterexample; accepted for publication at the New York Journal of Mathematics. arXiv admin note: text overlap with arXiv:1212.4529

References in corpus (4)

• Bimodules in bordered Heegaard Floer homology
• Fukaya categories of symmetric products and bordered Heegaard-Floer homology
• Bordered Floer homology for sutured manifolds
• The decategorification of bordered Heegaard Floer homology

Cited by in corpus (2)

• Floer Simple Manifolds and L-Space Intervals
• Bordered Floer homology with integral coefficients for manifolds with torus boundary