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An odd Khovanov homotopy type (1801.06308v2)
Published 19 Jan 2018 in math.GT
Abstract: For each link L in S3 and every quantum grading j, we construct a stable homotopy type Xj_o(L) whose cohomology recovers Ozsvath-Rasmussen-Szabo's odd Khovanov homology, H_i(Xj_o(L)) = Kh{i,j}_o(L), following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable homotopy type. Furthermore, the odd Khovanov homotopy type carries a Z/2 action whose fixed point set is a desuspension of the even Khovanov homotopy type. We also construct a Z/2 action on an even Khovanov homotopy type, with fixed point set a desuspension of Xj_o(L).