伪Anosov拉伸因子的代数次数
几何拓扑
2018-10-18 v6
摘要
本文的动机是证明Thurston的一个注记，即曲面上伪Anosov映射的拉伸因子的代数次数可以达到的Teichmüller空间的维数。除证明此结论外，我们几乎完全确定了所有有限型曲面上伪Anosov拉伸因子的可能代数次数集合。作为推论，我们找到了与闭可定向曲面的平面曲面Veech群的迹域相对应的数域的可能次数。我们的构造还给出了在给定曲面上寻找具有指定次数的拉伸因子的伪Anosov映射的算法。证明的一个要素是多项式的一个新型渐近不可约性判据。
引用
@article{arxiv.1506.06412,
title = {Algebraic degrees of pseudo-Anosov stretch factors},
author = {Balázs Strenner},
journal= {arXiv preprint arXiv:1506.06412},
year = {2018}
}
备注
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