Torsion Numbers of Augmented Groups

Susan G. Williams

KNOTS in WASHINGTON XIII; Conference on Knot Theory and its Ramifications
December 16, 2001
GWU
Washington, DC, USA

Organizers
Jozef H. Przytycki (GWU), Dubravko Ivansic (GWU)

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Torsion Numbers of Augmented Groups
by
Susan G. Williams
University of South Alabama
Coauthors: Daniel S. Silver (University of South Alabama)

Torsion and Betti numbers for knots are special cases of more general invariants b_r and \beta_r, respectively, associated to a finitely generated group G and epimorphism \chi: G → Z. The sequence of Betti numbers is always periodic; under mild hypotheses about (G, \chi), the sequence b_r satisfies a linear homogeneous recurrence relation with constant coefficients. Generally, b_r exhibits exponential growth rate. However, again under mild hypotheses, the p-part of b_r has trivial growth, for any prime p.

Date received: December 10, 2001