Hodge theory for complexes over \(C^\ast\)-algebras with an application to \(A\)-ellipticity

DOI10.1007/s10455-015-9449-1zbMath1328.58002arXiv1309.4560OpenAlexW3099440503MaRDI QIDQ2355549

Svatopluk Krýsl

Publication date: 24 July 2015

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.4560

zbMATH Keywords

\(C^\ast\)-Hilbert bundlesHilbert \(C^\ast\)-modulesHodge theoryelliptic systems of partial differential equations

Mathematics Subject Classification ID

(C^*)-modules (46L08) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Hodge theory in global analysis (58A14) Differential complexes (58J10) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18)

Related Items (3)

Induced \(C^*\)-complexes in metaplectic geometry ⋮ Elliptic complexes over \(C^\ast\)-algebras of compact operators ⋮ On the Chern-Gauss-Bonnet theorem and conformally twisted spectral triples for \(C^*\)-dynamical systems

Cites Work

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• Differential Analysis on Complex Manifolds
• The cohomology of Banach space bundles over 1–convex manifolds is not always Hausdorff
• On quantum and parallel transport in a Hilbert bundle over spacetime
• On quantum-geometric connections and propagators in curved spacetime

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