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.Comment: 64 pages, 19 figure