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Garland H, Raghunathan MS. Fundamental domains for lattices in rank one semisimple lie groups. Proc Natl Acad Sci U S A. 1969;62(2):309-13doi: 10.1073/pnas.62.2.309.
Garland, H., & Raghunathan, M. S. (1969). Fundamental domains for lattices in rank one semisimple lie groups. Proceedings of the National Academy of Sciences of the United States of America, 62(2), 309-13. https://doi.org/10.1073/pnas.62.2.309
Garland, H, and Raghunathan, M S. "Fundamental domains for lattices in rank one semisimple lie groups." Proceedings of the National Academy of Sciences of the United States of America vol. 62,2 (1969): 309-13. doi: https://doi.org/10.1073/pnas.62.2.309
Garland H, Raghunathan MS. Fundamental domains for lattices in rank one semisimple lie groups. Proc Natl Acad Sci U S A. 1969 Feb;62(2):309-13. doi: 10.1073/pnas.62.2.309. PMID: 16578691; PMCID: PMC277786.
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Proc Natl Acad Sci U S A. 1969 Feb;62(2):309-13. doi: 10.1073/pnas.62.2.309.

Fundamental domains for lattices in rank one semisimple lie groups.

Proceedings of the National Academy of Sciences of the United States of America

H Garland, M S Raghunathan

Affiliations

  1. YALE UNIVERSITY AND TATA INSTITUTE OF FUNDAMENTAL RESEARCH, BOMBAY, INDIA.

PMID: 16578691 PMCID: PMC277786 DOI: 10.1073/pnas.62.2.309

Abstract

We construct a fundamental domain omega for an arbitrary lattice [unk] in a real rank one, real simple Lie group, where omega has finitely many cusps (i.e., is a finite union of Siegel sets) and has the Siegel property (i.e., the set {gamma [unk] [unk]|omegagamma [unk] omega [unk] varphi} is finite). From the existence of omega we derive a number of consequences. In particular, we show that [unk] is finitely presentable and is almost always rigid.

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