New proofs of some results of Nielsen
New proofs of some results of Nielsen
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DOI：
10.1016/0001-8708(85)90028-3
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发表时间：
1985-05
影响因子：
1.7
通讯作者：
M. Handel;W. Thurston
中科院分区：
文献类型：
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作者：
M. Handel;W. Thurston
给定一个具有负欧拉特性和同胚 z: M2-+ M2 的紧致表面 M，s 的同位素类中最好的代表 cp: M2+ M2 是什么？ Thurston [S] 通过定义伪阿诺索夫同胚（T2 上阿诺索夫微分同胚的推广）回答了这个问题，其特征如下。同胚 rp 是伪阿诺索夫，当且仅当存在一对横向测量的测地线层压/i”和 AU，它们与 h4 中的每个闭合非外围测地线相交，它们（拓扑）由 cp 保留，并且对于某些 L> 1，它们各自的横向测量在 CP 的作用下乘以 l/n 和 d。Thurston 表明 cp: M*+ M2 可以从同胚拼凑在一起更准确地说，瑟斯顿证明了定理 0.1。预印本 [S] 介绍了该定理，描述了伪阿诺索夫微分同胚的许多有用属性。 [111] 中概述了该定理。
Given a compact oriented surface M with negative Euler characteristic and a homeomorphism z: M2-+ M2, what is the best representative cp: M2+ M2 in the isotopy class of s? Thurston [S] answered this question by defining pseudo-Anosov homeomorphisms (a generalization of Anosov diffeomorphisms on T2) which may be characterized as follows. The homeomorphism rp is pseudo-Anosov iff there is a pair of transverse measured geodesic laminations/i” and AU which intersect each closed nonperipheral geodesic in h4, which are (topologically) preserved by cp and which have their respective transverse measures multiplied under the action of CP by l/n and d for some L> 1.Thurston showed that cp: M*+ M2 can be pieced together from homeomorphisms of subsurfaces which are either periodic or pseudo-Anosov. More precisely, Thurston proved Theorem 0.1. The preprint [S] provides an introduction to this Theorem, describing many of the useful properties of pseudo-Anosov diffeomorphisms. The proof outlined in [S] is contained in [111.