Lehmer's question, knots and surface dynamics

2005/09/03 by Daniel S. Silver, Susan G. Williams, Silver, Daniel S. +1 · 1 citation
Computer Science · Mathematics · #11R06 #37C25 #57M25 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0509068

openalex publication_date 2005/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 injective free group endomorphisms.

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