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

S.M. Buckley; K. Falk

Analysis and Geometry in Metric Spaces (2014)

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

Abstract

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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

How to cite

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S.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

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  2. [2] K. Brown, ‘Buildings’, Springer-Verlag, Berlin, 1989. 
  3. [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. [4] S.M. Buckley and K. Falk, Natural maps between CAT(0) boundaries, New York J. Math. 19 (2013), 13-22. Zbl1279.51005
  5. [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. [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
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  9. [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. [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. [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. [12] G. Kasparov and G. Skandalis, Groupes ‘boliques’ et conjecture de Novikov, Comptes Rendus 158 (1994), 815-820. 
  13. [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. [14] J. Väisälä, Gromov hyperbolic spaces, Expo. Math. 23 (2005), no. 3, 187-231. Zbl1087.53039

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