# The Boundary at Infinity of a Rough CAT(0) Space

Analysis and Geometry in Metric Spaces (2014)

- Volume: 2, Issue: 1, page 53-80, electronic only
- ISSN: 2299-3274

## Access Full Article

top## Abstract

top## How to cite

topS.M. Buckley, and K. Falk. "The Boundary at Infinity of a Rough CAT(0) Space." Analysis and Geometry in Metric Spaces 2.1 (2014): 53-80, electronic only. <http://eudml.org/doc/267074>.

@article{S2014,

abstract = {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},

author = {S.M. Buckley, K. Falk},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {CAT(0) space; Gromov hyperbolic space; rough CAT(0) space; ideal boundary; Gromov boundary; bouquet boundary; space; rough space},

language = {eng},

number = {1},

pages = {53-80, electronic only},

title = {The Boundary at Infinity of a Rough CAT(0) Space},

url = {http://eudml.org/doc/267074},

volume = {2},

year = {2014},

}

TY - JOUR

AU - S.M. Buckley

AU - K. Falk

TI - The Boundary at Infinity of a Rough CAT(0) Space

JO - Analysis and Geometry in Metric Spaces

PY - 2014

VL - 2

IS - 1

SP - 53

EP - 80, electronic only

AB - 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

LA - eng

KW - CAT(0) space; Gromov hyperbolic space; rough CAT(0) space; ideal boundary; Gromov boundary; bouquet boundary; space; rough space

UR - http://eudml.org/doc/267074

ER -

## References

top- [1] M.R. Bridson and A. Haefliger, ‘Metric spaces of non-positive curvature’, Springer-Verlag, Berlin, 1999. Zbl0988.53001
- [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. Zbl1265.51011
- [4] S.M. Buckley and K. Falk, Natural maps between CAT(0) boundaries, New York J. Math. 19 (2013), 13-22. Zbl1279.51005
- [5] S.M. Buckley and B. Hanson, The n-point condition and rough CAT(0), Anal. Geom. Metric Spaces 1 (2012), 58-68. Zbl1262.30073
- [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. Zbl1182.54030
- [7] M. Coornaert, T. Delzant, and A. Papadopoulos, ‘Géometrie et théorie des groupes’, Lecture Notes in Mathematics 1441, Springer, Berlin, 1990. Zbl0727.20018
- [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. Zbl0731.20025
- [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. Zbl1044.20028
- [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. Zbl1029.19003
- [14] J. Väisälä, Gromov hyperbolic spaces, Expo. Math. 23 (2005), no. 3, 187-231. Zbl1087.53039

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.