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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