Noncommutative geometry of foliations

DOI10.1017/is008001006jkt029zbMath1155.58004arXivmath/0504095OpenAlexW1995726270MaRDI QIDQ3533788

Yurii A. Kordyukov

Publication date: 24 October 2008

Published in: Journal of K-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504095

zbMATH Keywords

foliationnon-commutative geometry\(K\)-theoryoperator algebracyclic cohomologyindex theory

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Noncommutative geometry (à la Connes) (58B34) Index theory (19K56)

Related Items (6)

Laplacians on Generalized Smooth Distributions as C Algebra Multipliers ⋮ The wave trace of the basic Laplacian of a Riemannian foliation near a non-zero period ⋮ Noncommutative Hamiltonian dynamics on foliated manifolds ⋮ Laplacians on smooth distributions ⋮ Laplacians on smooth distributions as \(C^*\)-algebra multipliers ⋮ Generalized symmetry in noncommutative (complex) geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The graph of a foliation
• Gravity coupled with matter and the foundation of non-commutative geometry
• Cyclic cohomology and the family Lefschetz theorem
• Secondary characteristic classes and cyclic cohomology of Hopf algebras
• Construction of universal bundles. I
• Rigidity theorems for foliations by surfaces and spin manifolds
• 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)
• A Lefschetz theorem for foliated manifolds
• \(K\)-theory. An introduction. With a new postface by the author and a list of errata
• The longitudinal index theorem for foliations
• Non-commutative differential geometry
• The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
• K-theory for the leaf space of foliations by Reeb components
• The action functional in non-commutative geometry
• An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R
• C*-algebras associated with irrational rotations
• The longitudinal cocycle and the index of Toeplitz operators
• Smooth dense subalgebras of reduced group \(C^*\)-algebras, Schwartz cohomology of groups, and cyclic cohomology
• Morita equivalence for C\(^*\)-algebras and W\(^*\)-algebras
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Currents, flows and diffeomorphisms
• Reduction of symplectic manifolds with symmetry
• Stable isomorphism and strong Morita equivalence of \(C^*\)-algebras
• The flow of weights on factors of type III
• Applications of Connes' geodesic flow to trace formulas in noncommutative geometry
• Hopf algebras, renormalization and noncommutative geometry
• The Novikov conjecture for hyperbolic foliations
• On the Hopf algebra strucutre of perturbative quantum field theories
• Hopf algebras, cyclic cohomology and the transverse index theorem
• Adiabatic limits and spectral geometry of foliations
• The Baum-Connes conjecture for amenable foliations
• Cyclic cohomology of étale groupoids: The general case
• The odd Chern character in cyclic homology and spectral flow
• Residue traces for certain algebras of Fourier integral operators
• Gauged Lagrangian distributions
• Cyclic cohomology of etale groupoids
• A longitudinal Lefschetz theorem in \(K\)-theory
• Čech-De Rham theory for leaf spaces of foliations
• A general families index theorem
• Stabilité des \(C^*\)-algèbres de feuilletages
• Geometry from the spectral point of view
• The local index formula in noncommutative geometry
• Bismut superconnections and the Chern character for Dirac operators on foliated manifolds
• The Godbillon-Vey cyclic cocycle and longitudinal Dirac operators
• Characters of cycles, equivariant characteristic classes and Fredholm modules
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• A new proof of Weyl's formula on the asymptotic distribution of eigenvalues
• The cohomology structure of an associative ring
• Local index theory over foliation groupoids
• The fundamental equations of a submersion
• A Lefschetz fixed point formula for elliptic complexes. I
• The index of elliptic operators. I
• Généralisation de la théorie de Morse aux variétés feuilletees
• The index of elliptic operators. IV, V
• Characteristic invariants of foliated bundles
• Transverse heat semigroup on the \(C^*\)-algebra of a Riemannian foliation
• Egorov's theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow
• Foliated manifolds with bundle-like metrics
• Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs. (Oka's principle, K-theory and noncommutative dynamical systems)
• Cyclic cocycles, renormalization and eta-invariants
• A new short proof of the local index formula and some of its applications.
• A higher Lefschetz formula for flat bundles
• Harmonic Integrals on Foliated Manifolds
• The $C^*$-algebras of codimension one foliations without holonomy.
• Secondary classes and transverse measure theory of a foliation
• Some Problems in Integral Geometry and Some Related Problems in Micro-Local Analysis
• On Coisotropic Imbeddings of Presymplectic Manifolds
• A SHORT PROOF THAT M_n(A) IS LOCAL IF A IS LOCAL AND FRÉCHET
• Characteristic Classes. (AM-76)
• Noncommutative Poisson Algebras
• Introduction to Algebraic K-Theory. (AM-72)
• Inner Product Modules Over B ∗ -Algebras
• On characteristic classes of $\Gamma $-foliations
• Foliation groupoids and their cyclic homology
• A Riemann-Roch theorem for one-dimensional complex groupoids.
• Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.
• Theory of operator algebras I.
• Introduction to M(atrix) theory and noncommutative geometry

This page was built for publication: Noncommutative geometry of foliations