Topology Atlas | Conferences

Knots in Washington XVII, Conference on Knot Theory and its Ramifications
December 19-21, 2003
GWU
Washington, DC, USA

Organizers
Marta M.Asaeda (U.Iowa), Mietek K.Dabkowski (UTD), Jozef H.Przytycki(GWU), Yongwu Rong (GWU)

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Skein theory for SU_n-quantum invariants
by
Adam S. Sikora
SUNY Buffalo and IAS

The Kauffman bracket skein relations provide an important method of studying SU_2-quantum invariants of links and 3-manifolds. Among its many applications, it makes possible to relate the SU_2-quantum invariants to Khovanov homology, skein modules, the (noncommutative) A-polynomial, and the SL_2-character varieties. In this talk, we discuss our skein calculus for SU_n-quantum invariants for all n, which hopefully has equally broad applications. Finally, we show that the SU_n-skein module of a 3-manifold M based on our skein relations is a q-deformation of the coordinate ring of the SL_n-character variety of pi_1(M).

Date received: November 12, 2003

Copyright © 2003 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 # camw-06.