Skein modules of links in cylinders over surfaces
Quantum Algebra
2009-09-25 v2
Abstract
We define the Conway skein module C(M) of ordered based links in a 3-manifold M. This module gives rise to C(M)-valued invariants of usual links in M. We determine a basis of the Z[z]-module C(F x [0,1])/Tor(C(F x [0,1])) where F is the real projective plane or a surface with boundary. For cylinders over the Moebius strip or the projective plane we derive special properties of the Conway skein module, including a refinement of a theorem of Kawauchi and Hartley about the Conway polynomial of strongly positive amphicheiral knots in S^3. We also determine the Homfly and Kauffman skein modules of F x [0,1] where F is an oriented surface with boundary.
Keywords
Cite
@article{arxiv.math/9911174,
title = {Skein modules of links in cylinders over surfaces},
author = {Jens Lieberum},
journal= {arXiv preprint arXiv:math/9911174},
year = {2009}
}
Comments
41 pages, 30 figures, new results added to previous version