Lehmer's question, knots and surface dynamics

Details Lehmer's question, knots and surface dynamics Lehmer's question, knots and surface dynamics

2005-09-03

arxiv.org/abs/math/0509068v3

Mathematics

Geometric Topology

Small corrections; to appear in Math. Proc. Cambridge Phil. Soc. 17 pages, 1 figure

Scientific paper

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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