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Compact quotients of Cahen-Wallach spaces
About this Title
Ines Kath, Institut für Mathematik und Informatik, der Ernst-Moritz-Arndt Universität Greifswald, Walther-Rathenau-Str. 47, D-17489 Greifswald, Germany and Martin Olbrich, Université du Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg
Publication: Memoirs of the American Mathematical Society
Publication Year:
2019; Volume 262, Number 1264
ISBNs: 978-1-4704-4103-6 (print); 978-1-4704-5501-9 (online)
DOI: https://doi.org/10.1090/memo/1264
Published electronically: December 19, 2019
MSC: Primary 22E40, 53C50; Secondary 53C35, 57S30
Table of Contents
Chapters
- 1. Introduction
- 2. Cahen-Wallach spaces
- 3. Discrete subgroups of the isometry group
- 4. Proper and cocompact actions on Cahen-Wallach spaces
- 5. The real case
- 6. Good subspaces and the imaginary case
- 7. The general case
- 8. Properties of compact quotients and their fundamental groups
Abstract
Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. We derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.- Louis Auslander, Bieberbach’s theorem on space groups and discrete uniform subgroups of Lie groups. II, Amer. J. Math. 83 (1961), 276–280. MR 123637, DOI 10.2307/2372956
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