Higher invariants in noncommutative geometry (Q3297182)

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Language	Label	Description	Also known as
English	Higher invariants in noncommutative geometry	scientific article

Statements

scholarly article

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Higher invariants in noncommutative geometry (English)

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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/1905.12632

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zbMATH Keywords

higher invariants in noncommutative geometry

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MaRDI profile type

MaRDI publication profile

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The signature package on Witt spaces

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The Novikov conjecture on Cheeger spaces

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The index of elliptic operators. I

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Rational group ring elements with kernels having irrational dimension

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The Borel conjecture for hyperbolic and CAT(0)-groups

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The \(K\)-theoretic Farrell-Jones conjecture for hyperbolic groups

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On the K-theory of groups with finite asymptotic dimension

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On asymptotic dimension of groups

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A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory

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Constructing group actions on quasi-trees and applications to mapping class groups

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The eta invariant and metrics of positive scalar curvature

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Uniform embeddings of bounded geometry spaces into reflexive Banach space

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A \(K\)-theoretic relative index theorem and Callias-type Dirac operators

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Arithmetic manifolds of positive scalar curvature

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Aperiodic Tilings, Positive Scalar Curvature, and Amenability of Spaces

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The integral \(K\)-theoretic Novikov conjecture for groups with finite asymptotic dimension

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Controlled algebra and the Novikov conjectures for \(K\)- and \(L\)-theory

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Bounded rigidity of manifolds and asymptotic dimension growth

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On Invariants of Hirzebruch and Cheeger-Gromov

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Higher <i>ρ</i> -invariants and the surgery structure set

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On the Chern character of \(\theta \) summable Fredholm modules

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Cyclic cohomology, the Novikov conjecture and hyperbolic groups

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Group cohomology with Lipschitz control and higher signatures

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Groups generated by reflections and aspherical manifolds not covered by Euclidean space

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Realizing the analytic surgery group of Higson and Roe geometrically. III: Higher invariants

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An etale approach to the Novikov conjecture

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On Novikov's conjecture for non-positively curved manifolds. I

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A Topological Analogue of Mostow's Rigidity Theorem

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Rigidity for aspherical manifolds with \(\pi_1\subset GL_m(\mathbb{R})\)

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Groups Not Acting on Manifolds

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Curvature, tangentiality, and controlled topology

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Random walk in random groups.

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The classification of simply connected manifolds of positive scalar curvature

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Positive scalar curvature and the Dirac operator on complete Riemannian manifolds

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A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings

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The Novikov conjecture for linear groups

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A notion of geometric complexity and its application to topological rigidity

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Discrete groups with finite decomposition complexity

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Geometry of the mapping class groups. I: Boundary amenability

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The strong Novikov conjecture for low degree cohomology

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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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Mapping surgery to analysis. I: Analytic signatures

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Mapping surgery to analysis. II: Geometric signatures

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Mapping surgery to analysis. III: Exact sequences

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\(K\)-homology, assembly and rigidity theorems for relative eta invariants

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Counterexamples to the Baum-Connes conjecture

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The integral Novikov conjectures for linear groups containing torsion elements

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$\ell {\textunderscore }p$ ($p>2$) does not coarsely embed into a Hilbert space

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Equivariant KK-theory and the Novikov conjecture

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

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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88)

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The Novikov conjecture and geometry of Banach spaces

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The mapping class group from the viewpoint of measure equivalence theory

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

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The Baum-Connes conjecture with coefficients for hyperbolic groups

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On the homotopy invariance of higher signatures for manifolds with boundary

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Rho-classes, index theory and Stolz’ positive scalar curvature sequence

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On higher eta-invariants and metrics of positive scalar curvature

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Spectral sections and higher Atiyah-Patodi-Singer index theory on Galois coverings

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Homotopy invariance of twisted higher signatures on manifolds with boundary

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Higher eta-invariants

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Delocalized \(L^2\)-invariants

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The Novikov conjecture for low degree cohomology classes

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The Baum-Connes conjecture for hyperbolic groups.

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Induction theorems for groups of homotopy manifold structures

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Group cohomology and the cyclic cohomology of crossed products

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Large scale geometry

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On quantitative operator \(K\)-theory

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Groups with torsion, bordism and rho invariants

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The surgery exact sequence, \(K\)-theory and the signature operator

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Singular spaces, groupoids and metrics of positive scalar curvature

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KK-groups of crossed products by groups acting on trees

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The Kadison-Kaplansky conjecture for word-hyperbolic groups

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New holomorphically closed subalgebras of \(C^*\)-algebras of hyperbolic groups

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On the localization algebra of Guoliang Yu

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Finite decomposition complexity and the integral Novikov conjecture for higher algebraic \(K\)-theory

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Coarse cohomology and index theory on complete Riemannian manifolds

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Hyperbolic groups have finite asymptotic dimension

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Positive Curvature, Partial Vanishing Theorems and Coarse Indices

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Higher $G$-indices and applications

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Uniform embeddings of hyperbolic groups in Hilbert spaces

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On the structure of manifolds with positive scalar curvature

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The coarse Baum-Connes conjecture and groupoids

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The Atiyah-Patodi-Singer index theorem for Dirac operators over \(C^*\)-algebras

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Localized index and \(L^2\)-Lefschetz fixed-point formula for orbifolds

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Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds

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Finite part of operator \(K\)-theory for groups finitely embeddable into Hilbert space and the degree of nonrigidity of manifolds

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Higher Index Theory

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

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

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Positive scalar curvature, higher rho invariants and localization algebras

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Higher rho invariants and the moduli space of positive scalar curvature metrics

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A relative higher index theorem, diffeomorphisms and positive scalar curvature

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Localization algebras and the 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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Positive scalar curvature and product formulas for secondary index invariants

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Mapping the surgery exact sequence for topological manifolds to analysis

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Identifiers

zbMATH Open document ID

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10.1007/978-3-030-29597-4_12

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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:3297182

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