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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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