Pentagon and hexagon equations following Furusho
HTML articles powered by AMS MathViewer
- by Dror Bar-Natan and Zsuzsanna Dancso
- Proc. Amer. Math. Soc. 140 (2012), 1243-1250
- DOI: https://doi.org/10.1090/S0002-9939-2011-10996-1
- Published electronically: August 5, 2011
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
- Dror Bar-Natan, On associators and the Grothendieck-Teichmuller group. I, Selecta Math. (N.S.) 4 (1998), no. 2, 183–212. MR 1669949, DOI 10.1007/s000290050029
- V. G. Drinfel′d, Quasi-Hopf algebras, Algebra i Analiz 1 (1989), no. 6, 114–148 (Russian); English transl., Leningrad Math. J. 1 (1990), no. 6, 1419–1457. MR 1047964
- V. G. Drinfel′d, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with $\textrm {Gal}(\overline \textbf {Q}/\textbf {Q})$, Algebra i Analiz 2 (1990), no. 4, 149–181 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 4, 829–860. MR 1080203
- 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
- Tu Quoc Thang Le and Jun Murakami, Representation of the category of tangles by Kontsevich’s iterated integral, Comm. Math. Phys. 168 (1995), no. 3, 535–562. MR 1328252
- T. Willwacher: M. Kontsevich’s graph complex and the Grothendieck-Teichmueller Lie algebra, arXiv:1009.1654.
Bibliographic 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