Torsion numbers of augmented groups: with applications to knots and links

Details Torsion numbers of augmented groups: with applications to knots and links Torsion numbers of augmented groups: with applications to knots and links

2002-02-19

arxiv.org/abs/math/0202197v2

Mathematics

Geometric Topology

24 pages, no figures. Small corrections and amplifications of previous version

Scientific paper

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.

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