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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

   

 

A Khovanov stable homotopy type


Authors: Robert Lipshitz and Sucharit Sarkar
Journal: J. Amer. Math. Soc. 27 (2014), 983-1042
MSC (2010): Primary 57M25, 55P42
Published electronically: April 22, 2014
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Abstract: Given a link diagram $ L$ we construct spectra $ \mathcal {X}_{\mathit {Kh}}^j(L)$ so that the Khovanov homology $ \mathit {K}^{i,j}(L)$ is isomorphic to the (reduced) singular cohomology $ \widetilde {H}^{i}(\mathcal {X}_{\mathit {Kh}}^j(L))$. The construction of $ \mathcal {X}_{\mathit {Kh}}^j(L)$ is combinatorial and explicit. We prove that the stable homotopy type of $ \mathcal {X}_{\mathit {Kh}}^j(L)$ depends only on the isotopy class of the corresponding link.


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Additional Information

Robert Lipshitz
Affiliation: Department of Mathematics, Columbia University, 2900 Broadway, New York, New York 10027
Email: lipshitz@math.columbia.edu

Sucharit Sarkar
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: sucharit@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2014-00785-2
PII: S 0894-0347(2014)00785-2
Received by editor(s): August 13, 2012
Received by editor(s) in revised form: May 23, 2013, July 9, 2013, and August 6, 2013
Published electronically: April 22, 2014
Additional Notes: The first author was supported by NSF grant number DMS-0905796 and a Sloan Research Fellowship.
The second author was supported by a Clay Mathematics Institute Postdoctoral Fellowship
Article copyright: © Copyright 2014 Robert Lipshitz and Sucharit Sarkar