The Novikov Conjecture, the Group of Volume Preserving Diffeomorphisms, and Hilbert-Hadamard Spaces

Jianchao Wu 吴健超  (Penn State University)

15:00-16:00, Jan 4, 2019   Science Building A510

Abstract:

The Novikov conjecture is a central problem in manifold topology. Noncommutative geometry provides a potent approach to tackle this conjecture. Using C*-algebraic and K-theoretic tools, we prove that the Novikov conjecture holds for any discrete group admitting an isometric and metrically proper action on an admissible Hilbert-Hadamard space, which is an infinite-dimensional analogue of complete simply connected nonpositively curved Riemannian manifolds. In particular, these groups include geometrically discrete subgroups of the group of volume preserving diffeomorphisms of a compact smooth manifold with a volume form. This is joint work with Sherry Gong and Guoliang Yu.

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