Geodesic
Tits rigidity of CAT(0) group boundaries
Chao, Khek1 ; Swenson, Eric2
1Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
2Mathematics Department, Brigham Young University, Provo, UT 84602, USA
Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 429-444
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We define Tits rigidity for visual boundaries of CAT(0) groups, and prove that the join of two Cantor sets and its suspension are Tits rigid.

DOI : 10.2140/agt.2015.15.429
Classification : 53C23, 20F67, 51F99
Keywords: CAT(0)

Chao, Khek  1   ; Swenson, Eric  2

1 Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
2 Mathematics Department, Brigham Young University, Provo, UT 84602, USA 
@article{10_2140_agt_2015_15_429,
     author = {Chao, Khek and Swenson, Eric},
     title = {Tits rigidity of {CAT(0)} group boundaries},
     journal = {Algebraic and Geometric Topology},
     pages = {429--444},
     year = {2015},
     volume = {15},
     number = {1},
     doi = {10.2140/agt.2015.15.429},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.429/}
}
TY  - JOUR
AU  - Chao, Khek
AU  - Swenson, Eric
TI  - Tits rigidity of CAT(0) group boundaries
JO  - Algebraic and Geometric Topology
PY  - 2015
SP  - 429
EP  - 444
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.429/
DO  - 10.2140/agt.2015.15.429
ID  - 10_2140_agt_2015_15_429
ER  - 
%0 Journal Article
%A Chao, Khek
%A Swenson, Eric
%T Tits rigidity of CAT(0) group boundaries
%J Algebraic and Geometric Topology
%D 2015
%P 429-444
%V 15
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.429/
%R 10.2140/agt.2015.15.429
%F 10_2140_agt_2015_15_429
Chao, Khek; Swenson, Eric. Tits rigidity of CAT(0) group boundaries. Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 429-444. doi: 10.2140/agt.2015.15.429

[1] W Ballmann, Lectures on spaces of nonpositive curvature, 25, Birkhäuser (1995)

[2] M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999)

[3] J W Cannon, Shrinking cell-like decompositions of manifolds: Codimension three, Ann. Math. 110 (1979) 83

[4] K L H Chao, CAT(0) spaces with boundary the join of two Cantor sets, Algebr. Geom. Topol. 14 (2014) 1107

[5] C B Croke, B Kleiner, Spaces with nonpositive curvature and their ideal boundaries, Topology 39 (2000) 549

[6] D P Guralnik, E L Swenson, A ‘transversal’ for minimal invariant sets in the boundary of a CAT(0) group, Trans. Amer. Math. Soc. 365 (2013) 3069

[7] W Hurewicz, H Wallman, Dimension theory, 4, Princeton Univ. Press (1941)

[8] R L Moore, Concerning the cut-points of continuous curves and of other closed and connected point-sets, Proc. Natl. Acad. Sci. USA 9 (1923) 101

[9] P Papasoglu, E Swenson, Boundaries and JSJ decompositions of CAT(0) groups, Geom. Funct. Anal. 19 (2009) 559

[10] K E Ruane, Dynamics of the action of a CAT(0) group on the boundary, Geom. Dedicata 84 (2001) 81

[11] K Ruane, CAT(0) groups with specified boundary, Algebr. Geom. Topol. 6 (2006) 633

[12] E L Swenson, A cut point theorem for CAT(0) groups, J. Differential Geom. 53 (1999) 327

Cité par Sources :