Comptes Rendus
Algèbre, Géométrie et Topologie
Local Limits of Connected Subgroups of SL 3 ()
[Limites Locales des Sous-groupes Connectés de SL 3 ()]
Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 363-376.

Dans cet article, nous décrivons les limites locaux sous conjugaison de tous les sous-groupes fermés connectés de SL 3 () dans la topologie de Chabauty.

In this paper we describe the local limits under conjugation of all closed connected subgroups of SL 3 () in the Chabauty topology.

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Révisé le :
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DOI : 10.5802/crmath.160

Nir Lazarovich 1 ; Arielle Leitner 2

1 Department of Mathematics, Technion, Haifa 32000 Israel
2 Faculty of Math and C.S., The Weizmann Institute of Science, 234 Herzl Street, Rehovot 7610001 Israel
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     author = {Nir Lazarovich and Arielle Leitner},
     title = {Local {Limits} of {Connected} {Subgroups} of {SL}${}_3(\protect \mathbb{R})$},
     journal = {Comptes Rendus. Math\'ematique},
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Nir Lazarovich; Arielle Leitner. Local Limits of Connected Subgroups of SL${}_3(\protect \mathbb{R})$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 4, pp. 363-376. doi : 10.5802/crmath.160. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.160/

[1] Martin R. Bridson; Pierre de la Harpe; Victor Kleptzyn The Chabauty Space of Closed Subgroups of the Three Dimensional Heisenberg Group, Pac. J. Math., Volume 240 (2009) no. 1, pp. 1-48 | DOI | MR | Zbl

[2] Richard D. Canary; David Bernard Alper Epstein; Paul Green Notes on Notes of Thurston. Analytical and Geometrical Aspects of Hyperbolic Spaces, London Mathematical Society Lecture Note Series, 111, Cambridge University Press, 1987

[3] Claude Chabauty Limits d’Ensembles et Géométries des Nombres, Bull. Math. Soc. France, Volume 78 (1950), pp. 142-151 | Zbl

[4] Corina Ciobotaru; Arielle Leitner; Alain Valette Chabauty Limits of Subgroups of SL n p (2018) (https://arxiv.org/abs/1711.04864)

[5] Daryl Cooper; Jeffrey Danciger; Anna Weinhard Limits of Geometries, Trans. Amer. Math.Soc., Volume 370 (2018) no. 9, pp. 6585-6627 | DOI | MR | Zbl

[6] Michel Coste An Introduction to O-minimal Geometry, 1999 (published by the Institut de Recherche Mathématiques de Rennes, https://gcomte.perso.math.cnrs.fr/M2/CosteIntroductionToOminimalGeo.pdf)

[7] Lou van den Dries Limit Sets in O-minimal structures, O-minimal Structures, Lisbon 2003 Proceedings of a Summer School by the European Research and Training Network RAAG (Lecture Notes in Real and Algebraic Geometry) (2003), pp. 159-214

[8] James M. G. Fell A Hausdorff Topology for the Closed Subsets of a Locally Compact Non-Hausdorff Space, Proc. Am. Math. Soc., Volume 13 (1962), pp. 472-476 | DOI | MR | Zbl

[9] Yves Guivarc’h; Lizhen Ji; John C. Taylor Compactifications of Symmetric Spaces, Progress in Mathematics, 156, Birkhäuser, 1998 | MR | Zbl

[10] Yves Guivarc’h; Bertrand Rémy Group-theoretic Compactification of Bruhat–Tits Buildings, Ann. Sci. Éc. Norm. Supér., Volume 39 (2006) no. 6, pp. 871-920 | DOI | MR | Zbl

[11] Thomas Haettel L’espace des Sous-groups Fermés du Groupe ×, Algebr. Geom. Topol., Volume 10 (2010) no. 3, pp. 1395-1415 | DOI | MR | Zbl

[12] Thomas Haettel Compactification Chabauty de l’Espace des Sous-groupes de Cartan de SL(n,), Math. Z., Volume 274 (2012), pp. 573-601 | DOI | MR

[13] Pierre de la Harpe Spaces of Closed Subgroups of Locally Compact Groups (2008) (https://arxiv.org/abs/0807.2030)

[14] John Hubbard; Ibrahim Pourezza The Space of Closed Subgroups of 2 , Topology, Volume 18 (1979), pp. 143-146 | MR | Zbl

[15] Benoît Kloeckner The Space of Closed Subgroups of n is Stratified and Simply Connected, J. Topol., Volume 2 (2009) no. 3, pp. 570-588 | DOI | MR | Zbl

[16] Arielle Leitner Limits Under Conjugacy of the Diagonal Subgroup in SL n (), Proc. Amer. Math. Soc., Volume 144 (2014) no. 2, pp. 3243-3254 | MR | Zbl

[17] Arielle Leitner Conjugacy limits of the diagonal Cartan subgroup in SL 3 (), Geom. Dedicata, Volume 160 (2016), pp. 135-149 | DOI | MR | Zbl

[18] Pavel Winternitz Subalgebras of Lie algebras. Example of sl(3,), Symmetry in physics. In memory of Robert T. Sharp. Proceedings of the workshop symmetries in physics, Montréal, Canada, September 12–14, 2002 (CRM Proceedings & Lecture Notes), Volume 34 (2004), pp. 215-227 | MR | Zbl

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