  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.
