Combinatorial tangle Floer homology

Ina Petkova; Vera Vértesi

doi:10.2140/gt.2016.20.3219

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Home > Journals > Geom. Topol. > Volume 20 > Issue 6 > Article

2016 Combinatorial tangle Floer homology

Ina Petkova, Vera Vértesi

Geom. Topol. 20(6): 3219-3332 (2016). DOI: 10.2140/gt.2016.20.3219

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Abstract

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.