Topology Atlas | Conferences

Knots in Washington XXXI; Categorification, Quandles, Quantum knots and Quantum computing
December 3-5, 2010
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU, NSF), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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The A-Polynomial, Reidemeister Torsion and Quantum Invariants
by
Joanna Kania-Bartoszynska
National Science Foundation
Coauthors: Charles D. Frohman

Given a knot K in the 3-sphere denote by T the torus which is the boundary of the complement of K. The conjugacy classes of SU(2)-representations of the fundamental group of T are called the pillowcase. We use the Reidemeister torsion to construct a seminorm on the coordinate ring of the pillowcase whose radical is the A-ideal of the knot. A global formula for integrating against the Reidemeister torsion allows us to interpret it in terms of quantum invariants of the knot complement.

Date received: November 29, 2010

Copyright © 2010 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 # cbbr-26.