An odd Khovanov homotopy type

Sucharit Sarkar; Christopher Scaduto; Matthew Stoffregen

doi:10.1016/j.aim.2020.107112

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arXiv · 1801.06308

An odd Khovanov homotopy type

Sucharit Sarkar·Christopher Scaduto·Matthew Stoffregen

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Abstract

For each link L in S^3 and every quantum grading j, we construct a stable homotopy type X^j_o(L) whose cohomology recovers Ozsvath-Rasmussen-Szabo's odd Khovanov homology, H_i(X^j_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 X^j_o(L).

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BibTeX RIS

Sucharit Sarkar, Christopher Scaduto, Matthew Stoffregen. 2018-01-19. An odd Khovanov homotopy type. https://doi.org/10.1016/j.aim.2020.107112

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