The n -Point Condition and Rough CAT(0)

Stephen M. Buckley; Bruce Hanson

Analysis and Geometry in Metric Spaces (2013)

  • Volume: 1, page 58-68
  • ISSN: 2299-3274

Abstract

top
We show that for n ≥ 5, a length space (X; d) satisfies a rough n-point condition if and only if it is rough CAT(0). As a consequence, we show that the class of rough CAT(0) spaces is closed under reasonably general limit processes such as pointed and unpointed Gromov-Hausdorff limits and ultralimits.

How to cite

top

Stephen M. Buckley, and Bruce Hanson. " The n -Point Condition and Rough CAT(0) ." Analysis and Geometry in Metric Spaces 1 (2013): 58-68. <http://eudml.org/doc/266990>.

@article{StephenM2013,
abstract = {We show that for n ≥ 5, a length space (X; d) satisfies a rough n-point condition if and only if it is rough CAT(0). As a consequence, we show that the class of rough CAT(0) spaces is closed under reasonably general limit processes such as pointed and unpointed Gromov-Hausdorff limits and ultralimits.},
author = {Stephen M. Buckley, Bruce Hanson},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {CAT(0) space; rough CAT(0) space; Gromov hyperbolic space; Gromov-Hausdorff limit; ultralimit; space; rough space},
language = {eng},
pages = {58-68},
title = { The n -Point Condition and Rough CAT(0) },
url = {http://eudml.org/doc/266990},
volume = {1},
year = {2013},
}

TY - JOUR
AU - Stephen M. Buckley
AU - Bruce Hanson
TI - The n -Point Condition and Rough CAT(0)
JO - Analysis and Geometry in Metric Spaces
PY - 2013
VL - 1
SP - 58
EP - 68
AB - We show that for n ≥ 5, a length space (X; d) satisfies a rough n-point condition if and only if it is rough CAT(0). As a consequence, we show that the class of rough CAT(0) spaces is closed under reasonably general limit processes such as pointed and unpointed Gromov-Hausdorff limits and ultralimits.
LA - eng
KW - CAT(0) space; rough CAT(0) space; Gromov hyperbolic space; Gromov-Hausdorff limit; ultralimit; space; rough space
UR - http://eudml.org/doc/266990
ER -

References

top
  1. S.M. Buckley and K. Falk, Rough CAT(0) Spaces, Bull. Math. Soc. Sci. Math. Roumanie 55 (103) (2012), 3–33. Zbl1265.51011
  2. S.M. Buckley and K. Falk, The boundary at infinity of a rough CAT(0) space, preprint. (Available at http://arxiv. org/pdf/1209.6557.pdf) Zbl1296.51023
  3. M.R. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature. Springer-Verlag, New York 1999. Zbl0988.53001
  4. M. Coornaert, T. Delzant, and A. Papadopoulos, ‘Géometrie et théorie des groupes’, Lecture Notes in Mathematics 1441, Springer, Berlin, 1990. Zbl0727.20018
  5. T. Delzant and M. Gromov, Courbure mésoscopique et théorie de la toute petite simplification, J. Topology 1 (2008), 804–836. 
  6. E. Ghys and P. de la Harpe (Eds.), ‘Sur les groupes hyperboliques d’aprés Mikhael Gromov’, Progress in Math. 38, Birkhäuser, Boston, 1990. Zbl0731.20025
  7. M. Gromov, Mesoscopic curvature and hyperbolicity in ‘Global differential geometry: the mathematical legacy of Alfred Gray’, 58–69, Contemp. Math. 288, Amer. Math. Soc., Providence, RI, 2001. Zbl1006.53036
  8. G. Kasparov and G. Skandalis, Groupes ‘boliques’ et conjecture de Novikov, Comptes Rendus 158 (1994), 815–820. Zbl0839.19003
  9. G. Kasparov and G. Skandalis, Groups acting properly on‘bolic’ spaces and the Novikov conjecture, Ann. Math. 158 (2003), 165–206. Zbl1029.19003
  10. J. Väisälä, Gromov hyperbolic spaces, Expo. Math. 23 (2005), no. 3, 187–231. Zbl1087.53039

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.