Algebraic degrees of pseudo-Anosov stretch factors
Abstract
The motivation for this paper is to justify a remark of Thurston that the algebraic degree of stretch factors of pseudo-Anosov maps on a surface can be as high as the dimension of the Teichm\"uller space of . In addition to proving this, we completely determine the set of possible algebraic degrees of pseudo-Anosov stretch factors on almost all finite type surfaces. As a corollary, we find the possible degrees of the number fields that arise as trace fields of Veech groups of flat surfaces homeomorphic to closed orientable surfaces. Our construction also gives an algorithm for finding a pseudo-Anosov map on a given surface whose stretch factor has a prescribed degree. One ingredient of the proofs is a novel asymptotic irreducibility criterion for polynomials.
Keywords
Cite
@article{arxiv.1506.06412,
title = {Algebraic degrees of pseudo-Anosov stretch factors},
author = {Balázs Strenner},
journal= {arXiv preprint arXiv:1506.06412},
year = {2018}
}
Comments
40 pages, 18 figures. v2: Minor improvements. v3: More general results (nonorientable surfaces, odd degrees), density of Galois conjugates moved to separate paper. v4: Revised intro. v5: Complete rewrite: simplified exposition and notation, cleaner organization, more general irreducibility lemma, two examples that were verified by computer are now verified without a computer. v6: published version