A special class of nilmanifolds admitting an Anosov diffeomorphism

被引：6

作者：

Dekimpe, K ^{[1
]}

Malfait, W ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, B-8500 Kortrijk, Belgium

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 07期

关键词：

Anosov diffeomorphism; nilmanifold; free 2-step nilpotent Lie algebra; hyperbolic automorphism;

D O I：

10.1090/S0002-9939-99-05337-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nilmanifold admits an Anosov diffeomorphism if and only if its fundamental group (which is finitely generated, torsion-free and nilpotent) supports an automorphism having no eigenvalues of absolute value one. Here we concentrate on nilpotency class 2 and fundamental groups whose commutator subgroup is of maximal torsion-free rank. We prove that the corresponding nilmanifold admits an Anosov diffeomorphism if and only if the torsion-free rank of the abelianization of its fundamental group is greater than or equal to 3.

引用

页码：2171 / 2179

页数：9