Geodesic
Quasiflats in CAT(0) 2–complexes
Bestvina, Mladen1 ; Kleiner, Bruce2 ; Sageev, Michah3
1Department of Mathematics, University of Utah, Salt Lake City, UT 84112-0090, United States
2Courant Institute of Mathematical Sciences, 251 Mercer St, New York, NY 10012, United States
3Department of Mathematics, Israel Institute of Technology, 32000 Haifa, Israel
Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2663-2676
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We show that if X is a piecewise Euclidean 2–complex with a cocompact isometry group, then every 2–quasiflat in X is at finite Hausdorff distance from a subset Q which is locally flat outside a compact set, and asymptotically conical.

DOI : 10.2140/agt.2016.16.2663
Classification : 20F65
Keywords: quasi-isometry, quasiflat, piecewise Euclidean complex

Bestvina, Mladen  1   ; Kleiner, Bruce  2   ; Sageev, Michah  3

1 Department of Mathematics, University of Utah, Salt Lake City, UT 84112-0090, United States
2 Courant Institute of Mathematical Sciences, 251 Mercer St, New York, NY 10012, United States
3 Department of Mathematics, Israel Institute of Technology, 32000 Haifa, Israel 
@article{10_2140_agt_2016_16_2663,
     author = {Bestvina, Mladen and Kleiner, Bruce and Sageev, Michah},
     title = {Quasiflats in {CAT(0)} 2{\textendash}complexes},
     journal = {Algebraic and Geometric Topology},
     pages = {2663--2676},
     year = {2016},
     volume = {16},
     number = {5},
     doi = {10.2140/agt.2016.16.2663},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.2663/}
}
TY  - JOUR
AU  - Bestvina, Mladen
AU  - Kleiner, Bruce
AU  - Sageev, Michah
TI  - Quasiflats in CAT(0) 2–complexes
JO  - Algebraic and Geometric Topology
PY  - 2016
SP  - 2663
EP  - 2676
VL  - 16
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.2663/
DO  - 10.2140/agt.2016.16.2663
ID  - 10_2140_agt_2016_16_2663
ER  - 
%0 Journal Article
%A Bestvina, Mladen
%A Kleiner, Bruce
%A Sageev, Michah
%T Quasiflats in CAT(0) 2–complexes
%J Algebraic and Geometric Topology
%D 2016
%P 2663-2676
%V 16
%N 5
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.2663/
%R 10.2140/agt.2016.16.2663
%F 10_2140_agt_2016_16_2663
Bestvina, Mladen; Kleiner, Bruce; Sageev, Michah. Quasiflats in CAT(0) 2–complexes. Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2663-2676. doi: 10.2140/agt.2016.16.2663

[1] J Behrstock, B Kleiner, Y Minsky, L Mosher, Geometry and rigidity of mapping class groups, Geom. Topol. 16 (2012) 781 | DOI

[2] M Bestvina, B Kleiner, M Sageev, The asymptotic geometry of right-angled Artin groups, I, Geom. Topol. 12 (2008) 1653 | DOI

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

[4] A Eskin, Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces, J. Amer. Math. Soc. 11 (1998) 321 | DOI

[5] A Eskin, B Farb, Quasi-flats and rigidity in higher rank symmetric spaces, J. Amer. Math. Soc. 10 (1997) 653 | DOI

[6] A Hatcher, Algebraic topology, Cambridge Univ. Press (2002)

[7] M Kapovich, B Leeb, Quasi-isometries preserve the geometric decomposition of Haken manifolds, Invent. Math. 128 (1997) 393 | DOI

[8] B Kleiner, U Lang, Quasi-minimizers in Hadamard spaces,

[9] B Kleiner, B Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. 86 (1997) 115

[10] G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973)

[11] X Xie, The Tits boundary of a CAT(0) 2–complex, Trans. Amer. Math. Soc. 357 (2005) 1627 | DOI

Cité par Sources :