The Novikov conjecture for linear groups
From MaRDI portal
Publication:2388282
DOI10.1007/s10240-005-0030-5zbMath1073.19003OpenAlexW2014561979WikidataQ103979864 ScholiaQ103979864MaRDI QIDQ2388282
Nigel Higson, Shmuel Weinberger, Erik Guentner
Publication date: 12 September 2005
Published in: Publications Mathématiques (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=PMIHES_2005__101__243_0
Noncommutative topology (46L85) (K)-theory and operator algebras (19K99) Eta-invariants, Chern-Simons invariants (58J28)
Related Items
INVARIANT EXPECTATIONS AND VANISHING OF BOUNDED COHOMOLOGY FOR EXACT GROUPS, The Novikov conjecture and extensions of coarsely embeddable groups, Boundary amenability of $Out(F_N)$, Quasi-representations of groups and two-homology, The coarse geometric Novikov conjecture and uniform convexity, The coarse Novikov conjecture for coarse fibrations over Banach spaces with property (H), On exactness and isoperimetric profiles of discrete groups, Groups of polynomial automorphisms of the plane, Finite part of operator \(K\)-theory for groups finitely embeddable into Hilbert space and the degree of nonrigidity of manifolds, Coarse geometry of Hecke pairs and the Baum-Connes conjecture, Bivariant \(K\)-theory with \(\mathbb{R}/\mathbb{Z}\)-coefficients and rho classes of unitary representations, Embeddings of von Neumann algebras into uniform Roe algebras and quasi-local algebras, Abelianization and fixed point properties of units in integral group rings, A quantitative relative index theorem and Gromov's conjectures on positive scalar curvature (with an appendix by Jinmin Wang and Zhizhang Xie), Positive scalar curvature metrics via end-periodic manifolds, The integral Novikov conjectures for linear groups containing torsion elements, Operator norm localization for linear groups and its application to \(K\)-theory, First \(\ell^2\)-Betti numbers and proper proximality, Property (đ) for Groups Graded by Root Systems, Simple Lie groups without the approximation property, Haagerup property for \(C^\ast\)-algebras and rigidity of \(C^\ast\)-algebras with property (T), On the structural theory of \(\mathrm{II}_1\) factors of negatively curved groups. II: Actions by product groups, Noncommutative \(L^{p}\)-spaces without the completely bounded approximation property, On rigidity of Roe algebras, Uniformly bounded representations and exact groups, Extreme cases of limit operator theory on metric spaces, Finiteâdimensional approximation properties for uniform Roe algebras, The BaumâConnes conjecture: an extended survey, Higher invariants in noncommutative geometry, Aspects of non positive curvature for linear groups with no infinite order unipotents, Isoperimetry of group actions., The primitive ideal space of the C*-algebra of the affine semigroup of algebraic integers, Obstructions to matricial stability of discrete groups and almost flat $K$-theory, On Ozawa kernels, Matrix algebra of sets and variants of decomposition complexity, Nonlinear spectral calculus and super-expanders, Exactness of locally compact groups, Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture, Permanence of metric sparsification property under finite decomposition complexity, Complexes and exactness of certain Artin groups., A notion of geometric complexity and its application to topological rigidity, Uniform embeddings of bounded geometry spaces into reflexive Banach space, Elliptic operators and higher signatures., \(C^\ast\)-algebraic higher signatures and an invariance theorem in codimension two, Exactness versus \(C^*\)-exactness for certain non-discrete groups, Cartan subalgebras in uniform Roe algebras, Property A and affine buildings, The Novikov conjecture, the group of volume preserving diffeomorphisms and Hilbert-Hadamard spaces, Ozawa's classđźfor locally compact groups and unique prime factorization of group von Neumann algebras, $K$-exact groups and coarsely embeddable groups, The Novikov conjecture, PoincarĂ© inequalities, embeddings, and wild groups, A metric approach to limit operators, Nonpositive curvature is not coarsely universal, On relative property (T) and Haagerupâs property, Commensurating actions for groups of piecewise continuous transformations, Relative Kazhdan Property, Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups, Von Neumann equivalence and group exactness
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Kazhdan groups acting on compact manifolds
- Equivariant KK-theory and the Novikov conjecture
- Groups acting on buildings, operator \(K\)-theory, and Novikov's conjecture
- An example of a non nuclear C*-algebra, which has the metric approximation property
- Bivariant \(K\)-theory and the Novikov conjecture
- The coarse Baum-Connes conjecture and groupoids
- Permanence properties of \(C^*\)-exact groups
- Computations of \(K\)- and \(L\)-theory of cocompact planar groups
- The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
- Amenability and exactness for dynamical systems and their đ¶*-algebras
- Homotopy invariance of η-invariants
- Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92)
- Spectral asymmetry and Riemannian Geometry. I
- Spectral asymmetry and Riemannian geometry. II
- Operator đŸ-theory for groups which act properly and isometrically on Hilbert space
- Amenable actions and exactness for discrete groups
- Constructions preserving Hilbert space uniform embeddability of discrete groups
- Linear groups of finite cohomological dimension
- \(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space
- Groups with the Haagerup property. Gromov's a-T-menability
- Exactness and the Novikov conjecture
- Jumps of the eta-invariant. (With an appendix by Shmuel Weinberger: Rationality of \(\rho\)-invariants)