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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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Pentagon and hexagon equations following Furusho
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by Dror Bar-Natan and Zsuzsanna Dancso PDF
Proc. Amer. Math. Soc. 140 (2012), 1243-1250

Abstract:

H. Furusho proved the beautiful result that of the three defining equations for associators, the pentagon implies the two hexagons. In this paper we present a simpler proof for this theorem (although our paper is less dense and hence only slightly shorter). In particular, we package the use of algebraic geometry and Groethendieck-Teichmüller groups into a useful and previously known principle, and, less significantly, we eliminate the use of spherical braids.
References
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  • Hidekazu Furusho, Pentagon and hexagon equations, Ann. of Math. (2) 171 (2010), no. 1, 545–556. MR 2630048, DOI 10.4007/annals.2010.171.545
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Additional Information
  • Dror Bar-Natan
  • Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
  • Email: drorbn@math.toronto.edu
  • Zsuzsanna Dancso
  • Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
  • Email: zsuzsi@math.toronto.edu
  • Received by editor(s): October 4, 2010
  • Received by editor(s) in revised form: December 11, 2010, and January 5, 2011
  • Published electronically: August 5, 2011
  • Communicated by: Gail R. Letzter
  • © Copyright 2011 By the authors under Creative Commons Attribution 3.0 License (CC B4 3.0)
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1243-1250
  • MSC (2010): Primary 17B37
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10996-1
  • MathSciNet review: 2869109