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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Categorified invariants and the braid group
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by John A. Baldwin and J. Elisenda Grigsby PDF
Proc. Amer. Math. Soc. 143 (2015), 2801-2814 Request permission

Abstract:

We investigate two “categorified” braid conjugacy class invariants, one coming from Khovanov homology and the other from Heegaard Floer homology. We prove that each yields a solution to the word problem but not the conjugacy problem in the braid group. In particular, our proof in the Khovanov case is completely combinatorial.
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Additional Information
  • John A. Baldwin
  • Affiliation: Department of Mathematics, 301 Carney Hall, Boston College, Chestnut Hill, Massachusetts 02467
  • MR Author ID: 772542
  • Email: john.baldwin@bc.edu
  • J. Elisenda Grigsby
  • Affiliation: Department of Mathematics, 301 Carney Hall, Boston College, Chestnut Hill, Massachusetts 02467
  • MR Author ID: 794424
  • Email: julia.grigsby@bc.edu
  • Received by editor(s): July 26, 2013
  • Received by editor(s) in revised form: February 3, 2014, and February 11, 2014
  • Published electronically: February 26, 2015
  • Additional Notes: The first author was partially supported by NSF grant number DMS-1104688
    The second author was partially supported by NSF grant number DMS-0905848 and NSF CAREER award DMS-1151671.
  • Communicated by: Daniel Ruberman
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 2801-2814
  • MSC (2010): Primary 20F36, 57M27, 57R58, 81R50
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12482-3
  • MathSciNet review: 3336606