Geometrization of the Strong Novikov Conjecture for residually finite groups

By G. Gong, Qin Wang, Guoliang Yu. 2008

91 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f58a435fcf83dab4bdb19eb9c11b81910dd6808a

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On rigidity of Roe algebras (2011, methodology): “We will use the following definition (due to Gong, Wang, and Yu [10]) as a crutch to Theorem 5.”
Higher rho invariants and the moduli space of positive scalar curvature metrics (2013, methodology): “In this paper, we will mainly work with the maximal Roe algebra [4].”
Geometric property (T) (2013, background): “In [18, Section 7], the current authors introduced geometric property (T): this is a pathological property of metric spaces designed to be an obstruction to the maximal version [8] of the coarse Baum-Connes conjecture in Ktheory and higher index theory.”
Metric sparsification and operator norm localization (2007, methodology): “Now the proof of Theorem 7.1 follows from our lemma and the argument in the proof of part III of Theorem 5.2 in [ 3 ].”
The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space (2012, methodology): “The following result is essentially proved in [11].”
On a quantitative operator K-theory (2011, unknown): “If X has bounded geometry, then the Roe algebra admits a maximal version [7] filtered by (C[X ]r)r>0.”
Higher index theory for certain expanders and Gromov monster groups I (2010, background): “the coarse Novikov conjecture), or of its maximal version, is known to be true for certain classes of expanders by work of Gong–Wang–Yu [15], Chen– Tessera–Wang–Yu [10], Guentner–Tessera–Yu [17] and Oyono-Oyono–Yu [32].”
Maximal and reduced Roe algebras of coarsely embeddable spaces (2011, background): “More recently, a maximal version of the Roe algebra, C∗ max(X), was introduced in work of Gong, Wang and Yu on the Baum-Connes and coarse Baum-Connes conjectures [7]; a maximal version of the uniform Roe algebra, C∗ u,max(X), can de defined analogously.”