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Noncommutative geometry of foliations (Q3533788)

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scientific article

Language	Label	Description	Also known as
English	Noncommutative geometry of foliations	scientific article

Statements

scholarly article

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Noncommutative geometry of foliations (English)

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publication date

24 October 2008

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full work available at URL

https://arxiv.org/abs/math/0504095

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zbMATH Keywords

\(K\)-theory

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non-commutative geometry

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foliation

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operator algebra

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cyclic cohomology

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index theory

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Yu. A. Kordyukov

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MaRDI profile type

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A Riemann-Roch theorem for one-dimensional complex groupoids.

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Inner Product Modules Over B ∗ -Algebras

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The fundamental equations of a submersion

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The $C^*$-algebras of codimension one foliations without holonomy.

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The Godbillon-Vey cyclic cocycle and longitudinal Dirac operators

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Characteristic Classes. (AM-76)

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Stabilité des \(C^*\)-algèbres de feuilletages

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Introduction to Algebraic K-Theory. (AM-72)

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A general families index theorem

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Rigidity theorems for foliations by surfaces and spin manifolds

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A Lefschetz theorem for foliated manifolds

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Bismut superconnections and the Chern character for Dirac operators on foliated manifolds

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Construction of universal bundles. I

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Reduction of symplectic manifolds with symmetry

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La conjecture de Baum-Connes pour un feuilletage sans holonomie de codimension un sur une variété fermée. (The Baum-Connes conjecture for a foliation without holonomy of codimension one in a closed manifold)

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Some Problems in Integral Geometry and Some Related Problems in Micro-Local Analysis

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Residue traces for certain algebras of Fourier integral operators

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Gauged Lagrangian distributions

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A new proof of Weyl's formula on the asymptotic distribution of eigenvalues

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On Coisotropic Imbeddings of Presymplectic Manifolds

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On the Hopf algebra strucutre of perturbative quantum field theories

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Egorov's theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow

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Adiabatic limits and spectral geometry of foliations

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Introduction to M(atrix) theory and noncommutative geometry

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Local index theory over foliation groupoids

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Secondary characteristic classes and cyclic cohomology of Hopf algebras

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Characters of cycles, equivariant characteristic classes and Fredholm modules

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Applications of Connes' geodesic flow to trace formulas in noncommutative geometry

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The odd Chern character in cyclic homology and spectral flow

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The cohomology structure of an associative ring

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\(K\)-theory. An introduction. With a new postface by the author and a list of errata

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Characteristic invariants of foliated bundles

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Smooth dense subalgebras of reduced group \(C^*\)-algebras, Schwartz cohomology of groups, and cyclic cohomology

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Secondary classes and transverse measure theory of a foliation

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The spectrum of positive elliptic operators and periodic bicharacteristics

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The longitudinal cocycle and the index of Toeplitz operators

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Cyclic cocycles, renormalization and eta-invariants

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Čech-De Rham theory for leaf spaces of foliations

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Foliation groupoids and their cyclic homology

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Cyclic cohomology of étale groupoids: The general case

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The flow of weights on factors of type III

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The longitudinal index theorem for foliations

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Hopf algebras, cyclic cohomology and the transverse index theorem

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The local index formula in noncommutative geometry

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Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.

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Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem

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Hopf algebras, renormalization and noncommutative geometry

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Gravity coupled with matter and the foundation of non-commutative geometry

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Geometry from the spectral point of view

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The action functional in non-commutative geometry

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Non-commutative differential geometry

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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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Cyclic cohomology of etale groupoids

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Stable isomorphism and strong Morita equivalence of \(C^*\)-algebras

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Noncommutative Poisson Algebras

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On characteristic classes of $\Gamma $-foliations

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The graph of a foliation

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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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The Novikov conjecture for hyperbolic foliations

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The Baum-Connes conjecture for amenable foliations

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The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs

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K-theory for the leaf space of foliations by Reeb components

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Généralisation de la théorie de Morse aux variétés feuilletees

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A higher Lefschetz formula for flat bundles

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Cyclic cohomology and the family Lefschetz theorem

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Theory of operator algebras I.

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A longitudinal Lefschetz theorem in \(K\)-theory

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The index of elliptic operators. IV, V

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A SHORT PROOF THAT M<sub>n</sub>(A) IS LOCAL IF A IS LOCAL AND FRÉCHET

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The index of elliptic operators. I

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Transverse heat semigroup on the \(C^*\)-algebra of a Riemannian foliation

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A Lefschetz fixed point formula for elliptic complexes. I

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Currents, flows and diffeomorphisms

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C*-algebras associated with irrational rotations

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Morita equivalence for C\(^*\)-algebras and W\(^*\)-algebras

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Harmonic Integrals on Foliated Manifolds

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Foliated manifolds with bundle-like metrics

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A new short proof of the local index formula and some of its applications.

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1017/IS008001006JKT029

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Sitelinks

Mathematics(1 entry)

mardi Publication:3533788

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