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


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.


Gennadi Kasparov

Institut de Mathématiques de Luminy, Marseille, France

Georges Skandalis

Institut de Mathématiques de Jussieu, Université Denis Diderot (Paris VII), Paris, France