Instantons and odd Khovanov homology

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.

64 pages, 19 figures

References in corpus (2)

• On the Khovanov and knot Floer homologies of quasi-alternating links
• Odd Khovanov homology is mutation invariant

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