English

Quantum gl(1|1) and tangle Floer homology

Geometric Topology 2020-02-25 v2 Quantum Algebra

Abstract

We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain Uq(gl(11))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 EE and FF of Uq(gl(11))U_q(gl(1|1)).

Keywords

Cite

@article{arxiv.1510.03483,
  title  = {Quantum gl(1|1) and tangle Floer homology},
  author = {Alexander P. Ellis and Ina Petkova and Vera Vértesi},
  journal= {arXiv preprint arXiv:1510.03483},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-22T11:18:37.921Z