dc.creator | Wu, Jianchao | |
dc.date.accessioned | 2020-08-22T20:32:48Z | |
dc.date.available | 2019-07-22 | |
dc.date.issued | 2019-07-22 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-07222019-112542 | |
dc.identifier.uri | http://hdl.handle.net/1803/13472 | |
dc.description.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. | |
dc.format.mimetype | application/pdf | |
dc.subject | C*-algebras | |
dc.subject | K-theory | |
dc.subject | noncommutative geometry | |
dc.subject | Novikov conjecture | |
dc.title | The Novikov Conjecture, the Group of Volume Preserving Diffeomorphisms and Non-Positively Curved Hilbert Manifolds | |
dc.type | dissertation | |
dc.contributor.committeeMember | Gennadi Kasparov | |
dc.contributor.committeeMember | Denis Osin | |
dc.contributor.committeeMember | Kalman Varga | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2019-07-22 | |
local.embargo.lift | 2019-07-22 | |
dc.contributor.committeeChair | Guoliang Yu | |