Slicing planar grid diagrams: a gentle introduction to bordered Heegaard Floer homology

Abstract

We describe some of the algebra underlying the decomposition of planar grid diagrams. This provides a useful toy model for an extension of Heegaard Floer homology to 3-manifolds with parametrized boundary. This paper is meant to serve as a gentle introduction to the subject, and does not itself have immediate topological applications.

25 pages, 9 figures

References in corpus (2)

• Floer homology and knot complements
• Bordered Heegaard Floer homology: Invariance and pairing

Cited by in corpus (5)

• An introduction to diagrammatic algebra and categorified quantum sl(2)
• An approach to categorification of some small quantum groups II
• Computations of Szabó's Geometric Spectral Sequence in Khovanov Homology
• A categorification of the positive half of quantum gl(m|1)
• Embedded and Lagrangian Knotted Tori in $\BR^4$ and Hypercube Homology