Torsion numbers of augmented groups: with applications to knots and links
Geometric Topology
2007-05-23 v2
Abstract
Torsion and Betti numbers for knots are special cases of more general invariants associated to a finitely generated group G and epimorphism from G to the integers. The sequence of Betti numbers is always periodic; under mild hypotheses, the sequence of torsion numbers satisfies a linear homogeneous recurrence relation with constant coeffiencts. Generally, the torsion number sequence exhibits exponential growth rate. However, again under mild hypotheses, the p-part has trivial growth for any prime p. Applications to branched cover homology for knots and links are presented.
Keywords
Cite
@article{arxiv.math/0202197,
title = {Torsion numbers of augmented groups: with applications to knots and links},
author = {Daniel S. Silver and Susan G. Williams},
journal= {arXiv preprint arXiv:math/0202197},
year = {2007}
}
Comments
24 pages, no figures. Small corrections and amplifications of previous version