Groups acting properly on “bolic” spaces and the Novikov conjecture

2003/07/01 by Gennadi Kasparov, Georges Skandalis · 2 citations
Mathematics · #Advanced Operator Algebra Research #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.4007/annals.2003.158.165

openalex publication_date 2003/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

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.

Cited by

• From acyclic groups to the Bass conjecture for amenable groups
• Georges Skandalis [wikipedia]