Atiyah covering index theorem for Riemannian foliations

DOI10.1090/tran/7731zbMath1419.19004arXiv1804.07033OpenAlexW2962679186WikidataQ115280407 ScholiaQ115280407MaRDI QIDQ4633609

Moulay Tahar Benameur, James L. Heitsch

Publication date: 3 May 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.07033

zbMATH Keywords

foliationsspectral triplesConnes-Chern character

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative geometry (à la Connes) (58B34) Index theory (19K56)

Cites Work

• Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
• A Lefschetz theorem for foliated manifolds
• Transversal Dirac families in Riemannian foliations
• The Novikov conjecture for hyperbolic foliations
• Hopf algebras, cyclic cohomology and the transverse index theorem
• Noncommutative spectral geometry of Riemannian foliations
• Geometric \(K\)-theory for Lie groups and foliations
• Transverse noncommutative geometry of foliations
• A symbol calculus for foliations
• The basic component of the mean curvature of Riemannian foliations
• The local index formula in noncommutative geometry
• The Egorov theorem for transverse Dirac-type operators on foliated manifolds
• Type II non-commutative geometry. I: Dixmier trace in von Neumann algebras
• Finiteness and tenseness theorems for Riemannian foliations
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