Topology Atlas | Conferences

KNOTS in WASHINGTON XII Conference on Knot Theory and its Ramifications
May 10-12, 2001
George Washington University
Washington, DC, USA

Organizers
Dubravko Ivansic, Ilya Kofman, Jozef H. Przytycki, Yongwu Rong, Akira Yasuhara

Conference Homepage


The cubic skein module, Fox 7-colorings and unknotting number.
by
Mike Veve
George Washington University

We analyse the cubic skein module S4, \infty(M) = RLfr/(Sub) where (Sub) is the submodule generated by a cubic relation b0L0 + b1L1+ b2L2 + b3L3 + b\inftyL\infty and the framing relation L(1) = aL. We assume a, b0, b3 are invertible in the ring of coefficients R. For a manifold M being a 3-sphere we conjecture that the skein module is generated by trivial links. We analyse coefficients for which the unknot is a free generator and the (2, 3)-move is changing the sign of the skein element. We notice that the a (2, 3)-move is preserving the Fox 7-colorings of a link. We sketch the idea how to apply Traczyk's method of studying unknotting number with the help of our cubic skein module (or polynomial in a reduced case).

Date received: May 18, 2001

Copyright © 2001 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 # cahj-18.