A Khovanov stable homotopy type

Lipshitz, Robert; Sarkar, Sucharit

doi:10.1090/S0894-0347-2014-00785-2

A Khovanov stable homotopy type
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by Robert Lipshitz and Sucharit Sarkar

J. Amer. Math. Soc. 27 (2014), 983-1042

DOI: https://doi.org/10.1090/S0894-0347-2014-00785-2

Published electronically: April 22, 2014

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Abstract:

Given a link diagram $L$ we construct spectra $\mathcal {X}_{Kh}^j(L)$ so that the Khovanov homology $K^{i,j}(L)$ is isomorphic to the (reduced) singular cohomology $\widetilde {H}^{i}(\mathcal {X}_{Kh}^j(L))$. The construction of $\mathcal {X}_{Kh}^j(L)$ is combinatorial and explicit. We prove that the stable homotopy type of $\mathcal {X}_{Kh}^j(L)$ depends only on the isotopy class of the corresponding link.

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