English

Instantons and odd Khovanov homology

Geometric Topology 2024-09-09 v3 Quantum Algebra

Abstract

We construct a spectral sequence from the reduced odd Khovanov homology of a link converging to the framed instanton homology of the double cover branched over the link, with orientation reversed. Framed instanton homology counts certain instantons on the cylinder of a 3-manifold connect-summed with a 3-torus. En route, we provide a new proof of Floer's surgery exact triangle for instanton homology using metric stretching maps, and generalize the exact triangle to a link surgeries spectral sequence. Finally, we relate framed instanton homology to Floer's instanton homology for admissible bundles.

Keywords

Cite

@article{arxiv.1401.2093,
  title  = {Instantons and odd Khovanov homology},
  author = {Christopher W. Scaduto},
  journal= {arXiv preprint arXiv:1401.2093},
  year   = {2024}
}

Comments

64 pages, 19 figures