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Spectral Sequences And Khovanov Homology, Zachary J. Winkeler
Spectral Sequences And Khovanov Homology, Zachary J. Winkeler
Dartmouth College Ph.D Dissertations
In this thesis, we will focus on two main topics; the common thread between both will be the existence of spectral sequences relating Khovanov homology to other knot invariants. Our first topic is an invariant MKh(L) for links in thickened disks with multiple punctures. This invariant is different from but inspired by both the Asaeda-Pryzytycki-Sikora (APS) homology and its specialization to links in the solid torus. Our theory will be constructed from a Z^n-filtration on the Khovanov complex, and as a result we will get various spectral sequences relating MKh(L) to Kh(L), AKh(L), and APS(L). Our …