Hyperbolic dimension of metric spaces

Details Hyperbolic dimension of metric spaces Hyperbolic dimension of metric spaces

2004-04-29

arxiv.org/abs/math/0404525v1

St. Petersburg Math. J. 19 (2008), no. 1, 67--76.

Mathematics

Geometric Topology

18 pages

Scientific paper

We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic dimension is at most the asymptotic dimension, however, unlike the asymptotic dimension, the hyperbolic dimension of any Euclidean space R^n is zero (while asdim R^n=n.) This invariant possesses usual properties of dimension like monotonicity and product theorems. Our main result says that the hyperbolic dimension of any Gromov hyperbolic space X (with mild restrictions) is at least the topological dimension of the boundary at infinity plus 1. As an application we obtain that there is no quasi-isometric embedding of the real hyperbolic space H^n into the (n-1)-fold metric product of metric trees stabilized by any Euclidean factor.

Affiliated with

Also associated with

No associations

Rating

Hyperbolic dimension of metric spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hyperbolic dimension of metric spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperbolic dimension of metric spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-567771