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Lehmer's Question, Knots and Surface Dynamics

Published online by Cambridge University Press:  01 November 2007

DANIEL S. SILVER  and
SUSAN G. WILLIAMS
DANIEL S. SILVER
Affiliation:
Department of Mathematics and Statistics University of South Alabama, Mobile, AL 36688, U.S.A.
SUSAN G. WILLIAMS*
Affiliation:
Department of Mathematics and Statistics University of South Alabama, Mobile, AL 36688, U.S.A.
*
†Both authors partially supported by NSF grant DMS-0304971.
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Abstract

Lehmer's question is equivalent to one about generalized growth rates of Lefschetz numbers of iterated pseudo-Anosov surface homeomorphisms. One need consider only homeomorphisms that arise as monodromies of fibered knots in lens spaces L(n, 1), n > 0. Lehmer's question for Perron polynomials is equivalent to one about generalized growth rates of words under free group endomorphisms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 3 , November 2007 , pp. 649 - 661
Copyright
Copyright © Cambridge Philosophical Society 2007

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