The Novikov conjecture and groups with finite asymptotic dimension ∗

Abstract

Recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology [14]. More precisely, the asymptotic dimension for a metric space is the smallest integer n such that for any r > 0, there exists a uniformly bounded cover C = {Ui}i∈I of the metric space for which the rmultiplicity of C is at most n + 1, i.e. no ball of radius r in the metric space intersects more than n + 1 members of C [14]. The class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space

Statistics

01020'98'00'02'04'06'08'10'12'14'16
Citations per Year

80 Citations

Semantic Scholar estimates that this publication has 80 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@inproceedings{Yu1998TheNC, title={The Novikov conjecture and groups with finite asymptotic dimension ∗}, author={Guoliang Yu}, year={1998} }