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Pentagon and hexagon equations following Furusho


Authors: Dror Bar-Natan and Zsuzsanna Dancso
Journal: Proc. Amer. Math. Soc. 140 (2012), 1243-1250
MSC (2010): Primary 17B37
DOI: https://doi.org/10.1090/S0002-9939-2011-10996-1
Published electronically: August 5, 2011
MathSciNet review: 2869109
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2011-10996-1
Keywords: Pentagon equation, hexagon equations, associators, Furusho’s theorem
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
Article copyright: © Copyright 2011 By the authors under Creative Commons Attribution 3.0 License (CC B4 3.0)

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