scientific article; zbMATH DE number 1518744

zbMath0958.46038MaRDI QIDQ4507229

Evgenij V. Troitsky, Yu. P. Solov'ev

Publication date: 17 October 2000

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

Novikov conjecturecyclic cohomologyBott periodicityConnes-Chern characterLefschetz numbersBruhat-Tits buildingFredholm representationshomotopy invariance of higher signatures\(C^\ast\)-Hilbert modules\(C^\ast\)-index theorem\(K\)-theory of \(C^*\)-bundlesFredholm theory in \(C^*\)-Hilbert modules

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) (C^*)-modules (46L08) (K)-theory and operator algebras (including cyclic theory) (46L80) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Differential topology (57R99) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Index theory (19K56) Pseudodifferential operators (47G30)

Related Items (12)

Analysis on singular spaces: Lie manifolds and operator algebras ⋮ Cohomology of the de Rham complex twisted by the oscillatory representation ⋮ Index of equivariant Callias-type operators and invariant metrics of positive scalar curvature ⋮ Induced \(C^*\)-complexes in metaplectic geometry ⋮ Hilbert schemes, Verma modules and spectral functions of hyperbolic geometry with application to quantum invariants ⋮ Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds ⋮ Hodge theory for elliptic complexes over unital \(C^\ast\)-algebras ⋮ An analogue of the Novikov Conjecture in complex algebraic geometry ⋮ Elliptic operators and higher signatures. ⋮ Elliptic complexes over \(C^\ast\)-algebras of compact operators ⋮ Hilbert \(C^*\) and \(W^*\)-modules and their morphisms ⋮ Hodge theory for complexes over \(C^\ast\)-algebras with an application to \(A\)-ellipticity

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