Groups acting properly on bolic spaces and the Novikov conjecture

• 成果类型: Article
• 署名作者: Kasparov, G; Skandalis, G
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2003.158.165
• 发表日期: 2003
• 页码: 165-206
• 关键词: baum-connes conjecture; EQUIVARIANT KK-THEORY; ALGEBRAS

摘要

We introduce a class of metric spaces which we call bolic. They include hyperbolic spaces, simply connected complete manifolds of nonpositive curvature, euclidean buildings, etc. We prove the Novikov conjecture on higher signatures for any discrete group which admits a proper isometric action on a bolic, weakly geodesic metric space of bounded geometry.