Metric sparsification and operator norm localization
By Xiaoman Chen, Romain Tessera, Xianjin Wang, Guoliang Yu. 2007
72 citations recorded by the source corpus.
Abstract We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. In particular, we introduce a sufficient geometric condition (called metric sparsification) for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that a sequence of expanding graphs does not possess the operator norm localization property.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/81d53b944a896dd5a1871631a324804d75a47e2d
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In Mathematical Physics
- Rufus Willett
- Ján Špakula
- Guoliang Yu
- Xiaoman Chen
- Qin Wang
- Hiroki Sako
- Martin Finn-Sell
- E. Guentner
Citations in the corpus
- On rigidity of Roe algebras (2011, background): “The papers [14, 20, 7, 8, 6, 29, 30, 34] contain more examples along these lines.”
- The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space (2012, background): “the injectivity of the assembly map μ, for a large class of expanders is proved in [6, 16, 32].”
- Higher index theory for certain expanders and Gromov monster groups I (2010, background): “• On the positive side, injectivity of the coarse assembly map (i.e. 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].”
- Property A and the operator norm localization property for discrete metric spaces (2012, background): “Yu defined the operator norm localization property in [4].”