On coarse geometric aspects of the Hilbert geometry
Metric Geometry
2017-05-02 v2
Abstract
We begin a coarse geometric study of Hilbert geometry. Actually we give a necessary and sufficient condition for the natural boundary of a Hilbert geometry to be a corona, which is a nice boundary in coarse geometry. In addition, we show that any Hilbert geometry is uniformly contractible and with coarse bounded geometry. As a consequence of these we see that the coarse Novikov conjecture holds for a Hilbert geometry with a mild condition. Also we show that the asymptotic dimension of any two-dimensional Hilbert geometry is just two. This implies that the coarse Baum-Connes conjecture holds for any two-dimensional Hilbert geometry via Yu's theorem.
Keywords
Cite
@article{arxiv.1412.5828,
title = {On coarse geometric aspects of the Hilbert geometry},
author = {Ryosuke Mineyama and Shin-ichi Oguni},
journal= {arXiv preprint arXiv:1412.5828},
year = {2017}
}
Comments
16 pages, 4 figures; changed the title and revised the introduction in ver 2