Operator norm localization for linear groups and its application to \(K\)-theory

DOI10.1016/j.aim.2010.10.022zbMath1222.46056OpenAlexW2077396983MaRDI QIDQ626118

Erik Guentner, Romain Tessera, Guo-Liang Yu

Publication date: 22 February 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2010.10.022

zbMATH Keywords

expandercoarse Novikov conjecturelinear groupbox spaceoperator norm localisation

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Residual properties and generalizations; residually finite groups (20E26) Index theory (19K56)

Related Items (11)

Expanders are counterexamples to the \(\ell^p\) coarse Baum-Connes conjecture ⋮ The equivariant coarse Novikov conjecture and coarse embedding ⋮ Spaces of graphs, boundary groupoids and the coarse Baum-Connes conjecture ⋮ The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space ⋮ Higher index theory for certain expanders and Gromov monster groups. I ⋮ Higher index theory for certain expanders and Gromov monster groups. II ⋮ Permanence of metric sparsification property under finite decomposition complexity ⋮ Operator norm localization property of metric spaces under finite decomposition complexity ⋮ Positive scalar curvature and a new index theory for noncompact manifolds ⋮ K-theory for the maximal Roe algebra of certain expanders ⋮ The coarse Novikov conjecture and Banach spaces with property (H)

Cites Work

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• A notion of geometric complexity and its application to topological rigidity
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• The Novikov conjecture for linear groups
• Comparing Analytic Assembly Maps
• Geometrization of the Strong Novikov Conjecture for residually finite groups
• Coarse cohomology and index theory on complete Riemannian manifolds
• Linear groups of finite cohomological dimension
• Permanence properties of the Baum-Connes conjecture

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