Combinatorial tangle Floer homology

Abstract

In this paper we extend the idea of bordered Floer homology to knots and links in $S^3$: Using a specific Heegaard diagram, we construct gluable combinatorial invariants of tangles in $S^3$, $D^3$ and $I\times S^2$. The special case of $S^3$ gives back a stabilized version of knot Floer homology.

106 pages, 44 figures

References in corpus (2)

• Knot Floer homology detects fibred knots
• The Alexander polynomial as quantum invariant of links

Cited by in corpus (6)

• Quantum gl(1|1) and tangle Floer homology
• Peculiar modules for 4-ended tangles
• Ozsvath-Szabo bordered algebras and subquotients of category O
• A quantum categorification of the Alexander polynomial
• Kauffman states and Heegaard diagrams for tangles
• Formal Contact Categories