The Boundary at Infinity of a Rough CAT(0) Space
S.M. Buckley ; K. Falk
Analysis and Geometry in Metric Spaces, Tome 2 (2014), / Harvested from The Polish Digital Mathematics Library

We develop the boundary theory of rough CAT(0) spaces, a class of length spaces that contains both Gromov hyperbolic length spaces and CAT(0) spaces. The resulting theory generalizes the common features of the Gromov boundary of a Gromov hyperbolic length space and the ideal boundary of a complete CAT(0) space. It is not assumed that the spaces are geodesic or proper

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267074
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     author = {S.M. Buckley and K. Falk},
     title = {The Boundary at Infinity of a Rough CAT(0) Space},
     journal = {Analysis and Geometry in Metric Spaces},
     volume = {2},
     year = {2014},
     zbl = {1296.51023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_agms-2014-0002}
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S.M. Buckley; K. Falk. The Boundary at Infinity of a Rough CAT(0) Space. Analysis and Geometry in Metric Spaces, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_agms-2014-0002/

[1] M.R. Bridson and A. Haefliger, ‘Metric spaces of non-positive curvature’, Springer-Verlag, Berlin, 1999. | Zbl 0988.53001

[2] K. Brown, ‘Buildings’, Springer-Verlag, Berlin, 1989.

[3] S.M. Buckley and K. Falk, Rough CAT(0) spaces, Bull. Math. Soc. Sci. Math. Roumanie 55 (103) (2012), 3-33. | Zbl 1265.51011

[4] S.M. Buckley and K. Falk, Natural maps between CAT(0) boundaries, New York J. Math. 19 (2013), 13-22. | Zbl 1279.51005

[5] S.M. Buckley and B. Hanson, The n-point condition and rough CAT(0), Anal. Geom. Metric Spaces 1 (2012), 58-68. | Zbl 1262.30073

[6] S.M. Buckley and S.L. Kokkendorff, Comparing the ideal and Floyd boundaries of a metric space, Trans. Amer.Math. Soc. 361 (2009), 715-734. | Zbl 1182.54030

[7] M. Coornaert, T. Delzant, and A. Papadopoulos, ‘Géometrie et théorie des groupes’, Lecture Notes in Mathematics 1441, Springer, Berlin, 1990. | Zbl 0727.20018

[8] T. Delzant and M. Gromov, Courbure mésoscopique et théorie de la toute petite simpliffcation, J. Topology 1 (2008), 804-836.

[9] E. Ghys and P. de la Harpe (Eds.), ‘Sur les groupes hyperboliques d’aprés Mikhael Gromov’, Progress in Mathematics 83, Birkhäuser, Boston, 1990. | Zbl 0731.20025

[10] M. Gromov,Mesoscopic curvature and hyperbolicity in ‘Global differential geometry: themathematical legacy of Alfred Gray’, 58-69, Contemp. Math. 288, Amer. Math. Soc., Providence, RI, 2001.

[11] I. Kapovich and N. Benakli, Boundaries of hyperbolic groups in ‘Combinatorial and geometric group theory’, 39-92, Contemp. Math. 296, Amer. Math. Soc., Providence, RI, 2002. | Zbl 1044.20028

[12] G. Kasparov and G. Skandalis, Groupes ‘boliques’ et conjecture de Novikov, Comptes Rendus 158 (1994), 815-820.

[13] G. Kasparov and G. Skandalis, Groups acting properly on ‘bolic’ spaces and the Novikov conjecture, Ann. Math. 158 (2003), 165-206. | Zbl 1029.19003

[14] J. Väisälä, Gromov hyperbolic spaces, Expo. Math. 23 (2005), no. 3, 187-231. | Zbl 1087.53039