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Organizers |
Almost extreme Khovanov homology of semi-adequate diagrams
by
Jozef H. Przytycki
George Washington University
Coauthors: Marithania Silvero (IMPA)
We say that (Xn, di) is a partial presimplicial set if
(1) (kXn, di) is a presimplicial module, that is didj=dj-1di for i < j, and
(2) for any xn ∈ Xn we have di(xn) ∈ Xn-1 or di(xn)=0.
Almost presimplicial set allows a standard geometric realization: if di(xn)=0 then the ith face of xn ×Δn is contracted. We show that almost extreme Khovanov homology of a A-adequate link can be obtained from an almost presimplicial set giving a finite CW complex geometric realization. In particular we show that for the trefoil knot its geometric realization is a projective plane, RP2. We conjecture that the geometric realization will be homotopy equivalent either to Sm or the suspension Σm-2RP2 depending on whether the B- state graph is bipartite or contains an odd cycle. m+1 is the number of crossings of considered link diagram. For example for the figure eight knot we obtain ΣRP2. We outline a proof of the conjecture which is based on the previous work of R.Sazdanovic and M.Silvero with the author.
Paper reference: arXiv:1608.03002 [math.GT], arXiv:1210.5254 [math.QA]
Date received: April 26, 2017
Copyright © 2017 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbof-25.