Dimension theory and large Riemannian manifolds
type: Item
instance of: scholarly article
title: Dimension theory and large Riemannian manifolds
zbMATH Open document ID: 0904.55001
published in: Documenta Mathematica
publication date: 1998-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/231645
full work available at URL: Dranishnikov.MAN.html
review text: This is an excellent write-up of a lucid lecture presented by the author at the ICM 98. It begins by an introduction to dimension theory (covering and cohomological) -- an area to which this author has contributed major discoveries in the last decade. The main part of the paper is devoted to recent applications of dimension theory to Novikov conjecture and related problems. A new approach is presented, based on the hypothetical equivalence between asymptotical dimension of a group and the covering dimension of its Higson corona.
Mathematics Subject Classification ID: 55M10
zbMATH DE Number: 1184320
zbMATH Keywords: cohomological dimension
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: Novikov conjecture
author: Alexander Dranishnikov
reviewed by: Dušan Repovš
MaRDI profile type: Publication
Recommended article: Cohomology, dimension and large Riemannian manifolds
Recommended article: Q3736498
Recommended article: On Gromov's large Riemannian manifolds
Recommended article: Riemannian and Finsler geometry in the large
Recommended article: Dimensions at infinity for Riemannian manifolds
Recommended article: Dimension, volume, and spectrum of a Riemannian manifold
Recommended article: On the theory of mappings of Riemannian manifolds ``in the large''
Recommended article: Large manifolds with positive Ricci curvature
Recommended article: Extremal manifolds and Hausdorff dimension
description: scientific article; zbMATH DE number 1184320