The Novikov Conjecture, the Group of Volume Preserving Diffeomorphisms and Non-Positively Curved Hilbert Manifolds
Wu, Jianchao
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2019-07-22
Abstract
We prove that the Novikov conjecture is satisfied by any discrete torsion-free group admitting an isometric and metrically proper action on a non-positively curved complete simply-connected Hilbert manifold with enough finite-dimensional complete geodesic submanifolds, under the assumption that this isometric action can be continuously deformed to the trivial action. The proof makes use of a C*-algebra associated to a non-positively curved simply-connected Hilbert manifold that generalizes a construction of Higson and Kasparov and parallels a construction of Kasparov and Yu.