A Khovanov stable homotopy type

Lipshitz, Robert¹ ; Sarkar, Sucharit²

¹ Department of Mathematics, Columbia University, 2900 Broadway, New York, New York 10027
² Department of Mathematics, Princeton University, Princeton, New Jersey 08544

Journal of the American Mathematical Society, Tome 27 (2014) no. 4, pp. 983-1042

Résumé

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.

Détail

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

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