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

DOI10.1016/0022-1236(85)90038-2zbMath0594.46062OpenAlexW1979378652MaRDI QIDQ1076948

Anne Marie Torpe

Publication date: 1985

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(85)90038-2

zbMATH Keywords

\(C^*\)-algebrashort exact sequencesK-theoryReeb foliation\(C^{\infty }\)-foliationsBaum-Connes' conjecturefoliations by Reeb componentsMayer-Vietoris and six-term exact sequences

Mathematics Subject Classification ID

Stable classes of vector space bundles in algebraic topology and relations to (K)-theory (55R50) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) General theory of (C^*)-algebras (46L05) Foliations in differential topology; geometric theory (57R30)

Related Items (8)

$C^*$-algebras of proper foliations ⋮ Noncommutative geometry of foliations ⋮ Noncommutative differential geometry on the quantum two sphere of Podlès. I: An algebraic viewpoint ⋮ The C*-algebras of Morse—Smale flows on two-manifolds ⋮ A Baum-Connes conjecture for singular foliations ⋮ The K-theory of the C*-algebra of foliations by slope components ⋮ The topology of foliations formed by the generic K-orbits of a subclass of the indecomposable \(\mathrm{MD}_{5}\)-groups ⋮ Non-commutative differential geometry

Cites Work

• The graph of a foliation
• The longitudinal index theorem for foliations
• The structure of imprimitivity algebras
• An analogue of the Thom isomorphism for crossed products of a C* algebra by an action of R
• Stable isomorphism and strong Morita equivalence of \(C^*\)-algebras
• Primitive ideals in enveloping algebras
• Induced representations of C\(^*\)-algebras
• Reeb foliations
• Un théorème de conjugaison des feuilletages
• Topological equivalence of Reeb foliations
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• The classification of extensions of 𝐶*-algebras
• Introduction to the Geometry of Foliations, Part A
• General Wiener-Hopf Operators
• Introduction to Algebraic K-Theory. (AM-72)
• Foliations
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