The space of closed subgroups of ℝn is stratified and simply connected

Journal of Topology

Volumn 2, Issue 3, 2009, Pages 570-588

  Kloeckner, Benoît ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77958085212     PISSN: 17538416     EISSN: 17538424     Source Type: Journal    
DOI: 10.1112/jtopol/jtp022     Document Type: Article

References (21)

1. A. Borel, L. Ji, Compactifications of symmetric and locally symmetric spaces, Mathematics: theory & applications, 2006, Boston, MA, Birkhäuser Boston Inc.
2. M. R. Bridson, P. de la Harpe, V. Kleptsyn, The Chabauty space of closed subgroups of the three-dimensional Heisenberg group, Pacific J. Math., 2009, 240, 1–48
3. C. Chabauty, Limite d'ensembles et géométrie des nombres, Bull. Soc. Math. France, 1950, 78, 143–151
4. P. de la Harpe, Spaces of closed subgroups of locally compact groups, Preprint, 2008, arXiv:0807.2030
5. C. Eyral, Profondeur homotopique et conjecture de Grothendieck, Ann. Sci. Éc. Norm. Supér., 2000, 33 (4), 823–836
6. M. Goresky, R. MacPherson, Intersection homology theory, Topology, 1980, 19, 135–162
7. M. Goresky, R. MacPherson, Intersection homology. II, Invent. Math., 1983, 72, 77–129
8. M. Goresky, R. MacPherson, Stratified Morse theory, 1988, Berlin, Springer, vol. 14 of Ergebnisse der Mathematik und ihrer Grenzgebiete 3 [Results in Mathematics and Related Areas 3]
9. R. M. Goresky, Triangulation of stratified objects, Proc. Amer. Math. Soc., 1978, 72, 193–200
10. Y. Guivarc'h, L. Ji, J. C. Taylor, Compactifications of symmetric spaces, 1998, 156, Boston, MA, Birkhäuser Boston Inc., Progress in Mathematics
11. Y. Guivarc'h, B. Rémy, Group-theoretic compactification of Bruhat-Tits buildings, Ann. Sci. Éc. Norm. Supér., 2006, 39 (4), 871–920
12. T. Haettel, Compactification de Chabauty des espaces symétriques de type non compact, Preprint, 2008, arXiv:0908.0208
13. T. Haettel, L'espace des sous-groupes fermés de ℝ × ℤ, Preprint, 2009, arXiv:0905.3290
14. F. E. A. Johnson, On the triangulation of stratified sets and singular varieties, Trans. Amer. Math. Soc., 1983, 275, 333–343
15. 2, Topology, 1979, 18, 143–146
16. I. Satake, On representations and compactifications of symmetric Riemannian spaces, Ann. of Math., 1960, 71 (2), 77–110
17. L. C. Siebenmann, Deformation of homeomorphisms on stratified sets, Comment. Math. Helv., 1972, 47, 123–136; 137–163, I, II
18. R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc., 1969, 75, 240–284
19. H. Whitney, Complexes of manifolds, Proc. Natl. Acad. Sci. USA, 1947, 33, 10–11
20. H. Whitney, Local properties of analytic varieties, Differential and combinatorial topology (a symposium in honor of Marston Morse), 1965, Princeton, NJ, Princeton University Press, 205–244
21. H. Whitney, Tangents to an analytic variety, Ann. of Math., 1965, 81 (2), 496–549