The Baum–Connes conjecture: an extended survey (Q3297174)

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English	The Baum–Connes conjecture: an extended survey	scientific article

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scholarly article

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The Baum–Connes conjecture: an extended survey (English)

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Maria Paula Gomez Aparicio

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Advances in Noncommutative Geometry

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publication date

3 July 2020

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full work available at URL

https://arxiv.org/abs/1905.10081

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zbMATH Keywords

groups

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\(C^*\)-algebras

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K-theory

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Baum-Connes conjecture

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MaRDI profile type

MaRDI publication profile

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The Cayley transform and uniformly bounded representations

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On the analogy between real reductive groups and Cartan motion groups: contraction of irreducible tempered representations

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Coarse non-amenability and coarse embeddings

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The index of elliptic operators. I

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A geometric construction of the discrete series for semisimple Lie groups

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Unbounded Negative Definite Functions

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Geometric \(K\)-theory for Lie groups and foliations

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Calculus on Heisenberg Manifolds. (AM-119)

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A Geometric Description of Equivariant K-Homology for Proper Actions

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\(C^*\)-simplicity and the unique trace property for discrete groups

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Unbounded symmetric operators in \(K\)-homology and the Baum-Connes conjecture

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Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs. (Oka's principle, K-theory and noncommutative dynamical systems)

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Harish-Chandra--Schwartz's algebras associated with discrete subgroups of Semisimple Lie groups

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Reductive groups over a local field

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Groups with the Haagerup property. Gromov's a-T-menability

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Deux remarques sur l'application de Baum–Connes

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The Connes-Kasparov conjecture for almost connected groups and for liner \(p\)-adic groups

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Pseudodifferential operators on groups with dilations

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Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one

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Property (RD) for cocompact lattices in a finite product of rank one Lie groups with some rank two Lie groups

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Complementary series of the Lorentz groups and \(KK\)-theory

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The \(L^2\)-index theorem for homogeneous spaces of Lie groups

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Cyclic cohomology, the Novikov conjecture and hyperbolic groups

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An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R

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Some geometric groups with rapid decay

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Curved Casimir operators and the BGG machinery

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Bernstein-Gelfand-Gelfand sequences

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Proper actions of wreath products and generalizations

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A characterization of relative Kazhdan property T for semidirect products with abelian groups

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The A-T-menability of some graphs of groups with cyclic edge groups

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Spaces over a category and assembly maps in isomorphism conjectures in \(K\)- and \(L\)-theory

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Strong property (T) for higher-rank simple Lie groups: Figure 1.

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Strong property (T) for higher rank lattices

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Superexpanders from group actions on compact manifolds

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Kazhdan projections, random walks and ergodic theorems

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Adiabatic groupoid, crossed product by \(\mathbb R_+^\ast\) and pseudodifferential calculus

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Survey of Oka theory

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Rigidity of warped cones and coarse geometry of expanders

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<i>K</i> ‐homology and <i>K</i> ‐theory for the lamplighter groups of finite groups

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Non-unitary representations, Baum-Connes morphism and unconditional completions

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Morphisme de Baum-Connes tordu par une représentation non unitaire

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Transformation de Poisson de formes différentielles. Le cas de l'espace hyperbolique. (Poisson transformation of differential forms. The case of hyperbolic space)

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The Novikov conjecture for linear groups

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Exactness and the Novikov conjecture

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Oka's Principle for Holomorphic Sections of Elliptic Bundles

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Random walk in random groups.

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Identifying assembly maps in \(K\)- and \(L\)-theory

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Geometry of the mapping class groups. I: Boundary amenability

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Bivariant \(K\)-theory and the Novikov conjecture

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\(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space

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Counterexamples to the Baum-Connes conjecture

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Amenable group actions and the Novikov conjecture

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An amenable group with a nonsymmetric group algebra

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Rapidly Decreasing Functions in Reduced C ∗ -Algebras of Groups

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The Baum-Connes conjecture with coefficients for the group \(\text{Sp}(n,1)\)

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How to prove the Baum-Connes conjecture for the groups \(S p(n, 1)\)?

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K-theoretic amenability for \(SL_ 2({\mathbb{Q}}_ p)\), and the action on the associated tree

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The Geometry of the Osculating Nilpotent Group Structures of the Heisenberg Calculus

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Operator \(K\)-theory and its applications

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Equivariant KK-theory and the Novikov conjecture

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The mapping class group from the viewpoint of measure equivalence theory

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Groups acting on buildings, operator \(K\)-theory, and Novikov's conjecture

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Groups acting properly on ``bolic'' spaces and the Novikov conjecture

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The coarse geometric Novikov conjecture and uniform convexity

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Bivariant \(K\)-theory for Banach algebras and the Baum-Connes conjecture

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K-THÉORIE BIVARIANTE POUR LES ALGÈBRES DE BANACH, GROUPOÏDES ET CONJECTURE DE BAUM–CONNES. AVEC UN APPENDICE D’HERVÉ OYONO-OYONO

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A reinforcement of property (T)

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PROPRIÉTÉ (T) RENFORCÉE BANACHIQUE ET TRANSFORMATION DE FOURIER RAPIDE

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The Baum-Connes conjecture with coefficients for hyperbolic groups

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The analytical assembly map and index theory

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Théorie de Kasparov équivariante et groupoïdes

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Equivariant Kasparov theory and groupoids. I

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Strong Banach property (T) for simple algebraic groups of higher rank

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About the obstacle to proving the Baum-Connes conjecture without coefficient for a non-cocompact lattice in \(Sp_4\) in a local field

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Group representations. A survey of some current topics

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Symmetry and nonsymmetry for locally compact groups

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Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski

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Variants of Kazhdan's property for subgroups of semisimple groups

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On embedding expanders into \(\ell_p\) spaces

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Straightening and bounded cohomology of hyperbolic groups

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Nonlinear spectral calculus and super-expanders

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Proper group actions and the Baum-Connes conjecture

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Relatively spectral morphisms and applications to K-theory

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Direct splitting method for the Baum-Connes conjecture

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Coarsely embeddable metric spaces without Property A

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Warped cones and spectral gaps

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Baum-Connes conjecture and group actions on trees

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Amenable actions and exactness for discrete groups

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K-theory for commutants in the Calkin algebra

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KK-groups of crossed products by groups acting on trees

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The tangent groupoid of a Heisenberg manifold

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The Dirac operator and the principal series for complex semisimple Lie groups

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The Baum-Connes conjecture with coefficients for word-hyperbolic groups (after Vincent Lafforgue)

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Coarse cohomology and index theory on complete Riemannian manifolds

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Warped cones and property A

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A Haagerup inequality for \(\widetilde A_1\times\widetilde A_1\) and \(\widetilde A_2\) buildings

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A ``stable'' version of the Gromov-Lawson conjecture

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Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie groups

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Finite group extensions and the Baum-Connes conjecture

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Bredon homology and equivariant \(K\)-homology of \(\mathrm{SL}(3,\mathbb Z)\)

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The coarse Baum-Connes conjecture and groupoids

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Topological Examples of Projective Modules

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The Baum-Connes conjecture and discrete group actions on trees

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The Baum-Connes conjecture for amenable foliations

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The Novikov conjecture for hyperbolic foliations

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<i>K</i>-THEORY FOR THE REDUCED C-ALGEBRA OF A SEMI-SIMPLE LIE GROUP WITH REAL RANK 1 AND FINITE CENTRE

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A groupoid approach to pseudodifferential calculi

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On the tangent groupoid of a filtered manifold

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Measure expanding actions, expanders and warped cones

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Representations of real reductive Lie groups

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PROPERTY A AND GRAPHS WITH LARGE GIRTH

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Higher index theory for certain expanders and Gromov monster groups. I

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Coarse Baum-Connes conjecture

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The Novikov conjecture for groups with finite asymptotic dimension

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The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space

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The Bernstein-Gelfand-Gelfand complex and Kasparov theory for \(SL(3,\mathbb C)\)

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Identifiers

zbMATH Open document ID

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10.1007/978-3-030-29597-4_3

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3297174

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