Then-Point Condition and Rough CAT(0)

• Autorzy: Stephen M. Buckley , Bruce Hanson
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

CAT(0) space; rough CAT(0) space; Gromov hyperbolic space; Gromov-Hausdorff limit; ultralimit

Kategorie tematyczne

• 30L05: Geometric embeddings of metric spaces
• 51M05: Euclidean geometries (general) and generalizations

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2013
• Tom: 1
• Strony: 58-68

Daty

otrzymano

2012-10-24

zaakceptowano

2012-12-24

online

2013-01-14

Twórcy

autor

Stephen M. Buckley

• Department of Mathematics and Statistics,
  National University of Ireland Maynooth, Maynooth, Co. KIldare, Ireland

autor

Bruce Hanson

• Department of Mathematics, Statistics and Computer
  Science, St. Olaf College, 1520 St. Olaf Avenue, Northfield, MN 55057, USA

Bibliografia

• S.M. Buckley and K. Falk, Rough CAT(0) Spaces, Bull. Math. Soc. Sci. Math. Roumanie 55 (103) (2012), 3–33.
• 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)
• M.R. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature. Springer-Verlag, New York 1999.
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• T. Delzant and M. Gromov, Courbure mésoscopique et théorie de la toute petite simplification, J. Topology 1 (2008), 804–836.
• E. Ghys and P. de la Harpe (Eds.), ‘Sur les groupes hyperboliques d’aprés Mikhael Gromov’, Progress in Math. 38, Birkhäuser, Boston, 1990.
• 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.
• G. Kasparov and G. Skandalis, Groupes ‘boliques’ et conjecture de Novikov, Comptes Rendus 158 (1994), 815–820.
• G. Kasparov and G. Skandalis, Groups acting properly on‘bolic’ spaces and the Novikov conjecture, Ann. Math. 158 (2003), 165–206.
• J. Väisälä, Gromov hyperbolic spaces, Expo. Math. 23 (2005), no. 3, 187–231.

Identyfikatory

DOI

10.2478/agms-2012-0005