The auslander conjecture for groups leaving a form of signature (n - 2, 2) invariant

H. Abels; G. A. Margulis; G. A. Soifer

doi:10.1007/bf02775430

The auslander conjecture for groups leaving a form of signature (n - 2, 2) invariant

H. Abels
, G. A. Margulis
, G. A. Soifer

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The Auslander conjecture claims that every affine crystallographic group τ is virtually solvable. We prove here this conjecture for the case when the linear part of τ is contained in the orthogonal group O(n - 2, 2).

Original language	English
Pages (from-to)	11-21
Number of pages	11
Journal	Israel Journal of Mathematics
Volume	148
DOIs	https://doi.org/10.1007/bf02775430
State	Published - 2005

Bibliographical note

Funding Information:
ACKNOWLEDGEMENT: The authors thank the following institutions for support: The Sonderforschungsbereich 343 Bielefeld and the Forschergruppe "Spec-trale Analysis, asymptotische Verteilungen und stochastische Dynamik" Biele-feld both financed by the Deutsche Forschungsgemeinschaft, the German-Israeli Foundation for Research and Development under Grant No. G-454-213.06/95, the NSF Grant DMS-0244406, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University, Center of Excellence ISF, grant N 8008/02-1 9 Our special thanks go to Gopal Prasad and Andrei Rapinchuk for providing the result \[PR\]w hich plays an essential role in our proof of Lemma 2.5.

Funding

ACKNOWLEDGEMENT: The authors thank the following institutions for support: The Sonderforschungsbereich 343 Bielefeld and the Forschergruppe "Spec-trale Analysis, asymptotische Verteilungen und stochastische Dynamik" Biele-feld both financed by the Deutsche Forschungsgemeinschaft, the German-Israeli Foundation for Research and Development under Grant No. G-454-213.06/95, the NSF Grant DMS-0244406, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University, Center of Excellence ISF, grant N 8008/02-1 9 Our special thanks go to Gopal Prasad and Andrei Rapinchuk for providing the result \[PR\]w hich plays an essential role in our proof of Lemma 2.5.

Funders	Funder number
Center of Excellence ISF	N 8008/02-1 9
Emmy Noether Research Institute for Mathematics
National Science Foundation	DMS-0244406
Deutsche Forschungsgemeinschaft
German-Israeli Foundation for Scientific Research and Development	G-454-213.06/95

Access to Document

10.1007/bf02775430

Cite this

@article{d1305532bcb340428fb2130d5141f666,

title = "The auslander conjecture for groups leaving a form of signature (n - 2, 2) invariant",

abstract = "The Auslander conjecture claims that every affine crystallographic group τ is virtually solvable. We prove here this conjecture for the case when the linear part of τ is contained in the orthogonal group O(n - 2, 2).",

author = "H. Abels and Margulis, \{G. A.\} and Soifer, \{G. A.\}",

note = "Funding Information: ACKNOWLEDGEMENT: The authors thank the following institutions for support: The Sonderforschungsbereich 343 Bielefeld and the Forschergruppe {"}Spec-trale Analysis, asymptotische Verteilungen und stochastische Dynamik{"} Biele-feld both financed by the Deutsche Forschungsgemeinschaft, the German-Israeli Foundation for Research and Development under Grant No. G-454-213.06/95, the NSF Grant DMS-0244406, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University, Center of Excellence ISF, grant N 8008/02-1 9 Our special thanks go to Gopal Prasad and Andrei Rapinchuk for providing the result \textbackslash{}[PR\textbackslash{}]w hich plays an essential role in our proof of Lemma 2.5.",

year = "2005",

doi = "10.1007/bf02775430",

language = "אנגלית",

volume = "148",

pages = "11--21",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

}

TY - JOUR

T1 - The auslander conjecture for groups leaving a form of signature (n - 2, 2) invariant

AU - Abels, H.

AU - Margulis, G. A.

AU - Soifer, G. A.

N1 - Funding Information: ACKNOWLEDGEMENT: The authors thank the following institutions for support: The Sonderforschungsbereich 343 Bielefeld and the Forschergruppe "Spec-trale Analysis, asymptotische Verteilungen und stochastische Dynamik" Biele-feld both financed by the Deutsche Forschungsgemeinschaft, the German-Israeli Foundation for Research and Development under Grant No. G-454-213.06/95, the NSF Grant DMS-0244406, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University, Center of Excellence ISF, grant N 8008/02-1 9 Our special thanks go to Gopal Prasad and Andrei Rapinchuk for providing the result \[PR\]w hich plays an essential role in our proof of Lemma 2.5.

PY - 2005

Y1 - 2005

N2 - The Auslander conjecture claims that every affine crystallographic group τ is virtually solvable. We prove here this conjecture for the case when the linear part of τ is contained in the orthogonal group O(n - 2, 2).

AB - The Auslander conjecture claims that every affine crystallographic group τ is virtually solvable. We prove here this conjecture for the case when the linear part of τ is contained in the orthogonal group O(n - 2, 2).

UR - https://www.scopus.com/pages/publications/32544448644

U2 - 10.1007/bf02775430

DO - 10.1007/bf02775430

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:32544448644

SN - 0021-2172

VL - 148

SP - 11

EP - 21

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

The auslander conjecture for groups leaving a form of signature (n - 2, 2) invariant

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this