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

Daniel S. Silver; Susan G. Williams

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arXiv · math/0202197

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

Daniel S. Silver·Susan G. Williams

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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.

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Daniel S. Silver, Susan G. Williams. 2002-08-06. Torsion numbers of augmented groups: with applications to knots and links. https://arxiv.org/abs/math/0202197

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