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Categorified invariants and the braid group


Authors: John A. Baldwin and J. Elisenda Grigsby
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
Published electronically: February 26, 2015
MathSciNet review: 3336606
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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
Email: john.baldwin@bc.edu

J. Elisenda Grigsby
Affiliation: Department of Mathematics, 301 Carney Hall, Boston College, Chestnut Hill, Massachusetts 02467
Email: julia.grigsby@bc.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12482-3
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
Article copyright: © Copyright 2015 American Mathematical Society