Algebraic Anosov actions of nilpotent Lie groups

被引：5

作者：

Barbot, Thierry ^{[1
]}

Maquera, Carlos ^{[2
]}

机构：

[1] Univ Avignon & Pays Vaucluse, LANLG, Fac Sci, F-84000 Avignon, France

[2] Univ Sao Paulo, Inst Ciencias Mat & Comp, BR-13560970 Sao Carlos, SP, Brazil

来源：

TOPOLOGY AND ITS APPLICATIONS | 2013年 / 160卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Algebraic Anosov action; Cartan subalgebra; CLASSIFICATION;

D O I：

10.1016/j.topol.2012.10.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we classify algebraic Anosov actions of nilpotent Lie groups on closed manifolds, extending the previous results by P. Tomter (1970, 1975)[17,18]. We show that they are all nil-suspensions over either suspensions of Anosov actions of Z(k) on nilmanifolds, or (modified) Weyl chamber actions. We check the validity of the generalized Verjovsky conjecture in this algebraic context. We also point out an intimate relation between algebraic Anosov actions and Cartan subalgebras in general real Lie groups. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：199 / 219

页数：21

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