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Knots in Washington XXXIII; Categorification of Knots, Algebras, and Quandles; Quantum Computing
December 2-4, 2011
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU),Mark Kidwell (U.S. Naval Academy and GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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The Andersen-Mattes-Reshetikhin Bracket Counts Intersections
by
Patricia Cahn
Dartmouth College
Coauthors: Vladimir Chernov

Andersen, Mattes, and Reshetikhin defined a Poisson algebra structure on a quotient of the free module generated by homotopy classes of chord diagrams on an oriented surface. We show that the number of terms in the Poisson bracket of two free homotopy classes A and B is equal to the minimum number of intersection points of loops in the classes A and B when A and B are not equal. This generalizes work of Goldman and Chas. In particular, Chas showed that a similar statement does not hold for the Goldman bracket unless one of the classes A or B is simple.

Date received: November 26, 2011

Copyright © 2011 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbdt-30.