TORSION NUMBERS OF AUGMENTED GROUPS with applications to knots and links
نویسندگان
چکیده
ABSTRACT. Torsion and Betti numbers for knots are special cases of more general invariants br and βr, respectively, associated to a finitely generated group G and epimorphism χ : G → Z. The sequence of Betti numbers is always periodic; under mild hypotheses about (G,χ), the sequence br satisfies a linear homogeneous recurrence relation with constant coefficients. Generally, br exhibits exponential growth rate. However, again under mild hypotheses, the p-part of br has trivial growth for any prime p. Applications to branched cover homology for knots and links are presented.
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