Properly discontinuous groups of affine transformations: A survey

被引：42

作者：

Abels, H ^{[1
]}

机构：

[1] Univ Bielefeld, Fac Math, D-33501 Bielefeld, Germany

来源：

GEOMETRIAE DEDICATA | 2001年 / 87卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

properly discontinuous groups; crystallographic groups; Auslander's conjecture; Milnor's question; flat affine manifolds;

D O I：

10.1023/A:1012019004745

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this survey article we discuss the structure of properly discontinuous groups of affine transformations and in particular of affine crystallographic groups. One of the main open questions is Auslander's conjecture claiming that every affine crystallographic group is virtually solvable.

引用

页码：309 / 333

页数：25

共 47 条

[1] INVARIANT SUBSPACES OF AFFINE GROUPS - AN ALGEBRAIC VERSION OF A THEOREM OF BIEBERBACH [J].

ABELS, H ;

DRESS, AWM .

JOURNAL OF ALGEBRA, 1986, 99 (02) :496-517

[2]

Abels H, 1999, J LIE THEORY, V9, P351

[3]

Abels H, 1997, CR ACAD SCI I-MATH, V324, P253

[4] SEMIGROUPS CONTAINING PROXIMAL LINEAR-MAPS [J].

ABELS, H ;

MARGULIS, GA ;

SOIFER, GA .

ISRAEL JOURNAL OF MATHEMATICS, 1995, 91 (1-3) :1-30

[5]

ABELS H, 97083 SFB

[6]

[Anonymous], NACHR GESELL WISS MP

[7]

[Anonymous], ELECT RES ANNOUNC AM

[8]

[Anonymous], CONT MATH

[9]

[Anonymous], ENSEIGN MATH

[10] SIMPLY TRANSITIVE GROUPS OF AFFINE MOTIONS [J].

AUSLANDER, L .

AMERICAN JOURNAL OF MATHEMATICS, 1977, 99 (04) :809-826

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