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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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A Khovanov stable homotopy type
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by Robert Lipshitz and Sucharit Sarkar PDF
J. Amer. Math. Soc. 27 (2014), 983-1042

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.
References
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Additional Information
  • Robert Lipshitz
  • Affiliation: Department of Mathematics, Columbia University, 2900 Broadway, New York, New York 10027
  • MR Author ID: 792304
  • Email: lipshitz@math.columbia.edu
  • Sucharit Sarkar
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 740423
  • Email: sucharit@math.princeton.edu
  • 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
  • © Copyright 2014 Robert Lipshitz and Sucharit Sarkar
  • Journal: J. Amer. Math. Soc. 27 (2014), 983-1042
  • MSC (2010): Primary 57M25, 55P42
  • DOI: https://doi.org/10.1090/S0894-0347-2014-00785-2
  • MathSciNet review: 3230817