Dans cet article, nous décrivons les limites locaux sous conjugaison de tous les sous-groupes fermés connectés de dans la topologie de Chabauty.
In this paper we describe the local limits under conjugation of all closed connected subgroups of in the Chabauty topology.
@article{CRMATH_2021__359_4_363_0, author = {Nir Lazarovich and Arielle Leitner}, title = {Local {Limits} of {Connected} {Subgroups} of {SL}${}_3(\protect \mathbb{R})$}, journal = {Comptes Rendus. Math\'ematique}, pages = {363--376}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {4}, year = {2021}, doi = {10.5802/crmath.160}, zbl = {07362158}, language = {en}, }
TY - JOUR AU - Nir Lazarovich AU - Arielle Leitner TI - Local Limits of Connected Subgroups of SL${}_3(\protect \mathbb{R})$ JO - Comptes Rendus. Mathématique PY - 2021 SP - 363 EP - 376 VL - 359 IS - 4 PB - Académie des sciences, Paris DO - 10.5802/crmath.160 LA - en ID - CRMATH_2021__359_4_363_0 ER -
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] 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] Notes on Notes of Thurston. Analytical and Geometrical Aspects of Hyperbolic Spaces, London Mathematical Society Lecture Note Series, 111, Cambridge University Press, 1987
[3] Limits d’Ensembles et Géométries des Nombres, Bull. Math. Soc. France, Volume 78 (1950), pp. 142-151 | Zbl
[4] Chabauty Limits of Subgroups of (2018) (https://arxiv.org/abs/1711.04864)
[5] Limits of Geometries, Trans. Amer. Math.Soc., Volume 370 (2018) no. 9, pp. 6585-6627 | DOI | MR | Zbl
[6] 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] 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] 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] Compactifications of Symmetric Spaces, Progress in Mathematics, 156, Birkhäuser, 1998 | MR | Zbl
[10] Group-theoretic Compactification of Bruhat–Tits Buildings, Ann. Sci. Éc. Norm. Supér., Volume 39 (2006) no. 6, pp. 871-920 | DOI | MR | Zbl
[11] L’espace des Sous-groups Fermés du Groupe , Algebr. Geom. Topol., Volume 10 (2010) no. 3, pp. 1395-1415 | DOI | MR | Zbl
[12] Compactification Chabauty de l’Espace des Sous-groupes de Cartan de , Math. Z., Volume 274 (2012), pp. 573-601 | DOI | MR
[13] Spaces of Closed Subgroups of Locally Compact Groups (2008) (https://arxiv.org/abs/0807.2030)
[14] The Space of Closed Subgroups of , Topology, Volume 18 (1979), pp. 143-146 | MR | Zbl
[15] The Space of Closed Subgroups of is Stratified and Simply Connected, J. Topol., Volume 2 (2009) no. 3, pp. 570-588 | DOI | MR | Zbl
[16] Limits Under Conjugacy of the Diagonal Subgroup in , Proc. Amer. Math. Soc., Volume 144 (2014) no. 2, pp. 3243-3254 | MR | Zbl
[17] Conjugacy limits of the diagonal Cartan subgroup in , Geom. Dedicata, Volume 160 (2016), pp. 135-149 | DOI | MR | Zbl
[18] Subalgebras of Lie algebras. Example of , 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
Cité par Sources :
Commentaires - Politique