Quantum gl(1|1) and tangle Floer homology

Abstract

We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain $U_q(gl(1|1))$ representations. Under this identification, up to a scalar factor, the map on the Grothendieck group induced by the tangle Floer dg bimodule associated to a tangle agrees with the Reshetikhin-Turaev homomorphism for that tangle. We also introduce dg bimodules which act on the Grothendieck group as the generators $E$ and $F$ of $U_q(gl(1|1))$.

56 pages, many EPS figures; improved exposition, corrected small mistakes

References in corpus (10)

• Floer homology and knot complements
• 2-Kac-Moody algebras
• Knot invariants and higher representation theory
• Bordered Floer homology for sutured manifolds
• The Alexander polynomial as quantum invariant of links
• On the skein exact squence for knot Floer homology
• A categorification of U_q sl(1,1) as an algebra
• The differential graded odd nilHecke algebra
• Combinatorial tangle Floer homology
• An introduction to tangle Floer homology

Cited by in corpus (8)

• Peculiar modules for 4-ended tangles
• DG structures on odd categorified quantum sl(2)
• Ozsvath-Szabo bordered algebras and subquotients of category O
• A quantum categorification of the Alexander polynomial
• From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron
• A self-pairing theorem for tangle Floer homology
• Trivalent vertices and bordered knot Floer homology in the standard basis
• Strands algebras and the affine highest weight property for equivariant hypertoric categories