Finite propagation speed and Connes' foliation algebra

DOI10.1017/S0305004100067517zbMath0646.58024OpenAlexW2025209618MaRDI QIDQ3790356

John Roe

Publication date: 1987

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100067517

zbMATH Keywords

Connes' index theoremspectral function of leafwise elliptic operators

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Hyperbolic equations on manifolds (58J45)

Related Items (20)

Getzler rescaling via adiabatic deformation and a renormalized index formula ⋮ Cyclic cocycles, renormalization and eta-invariants ⋮ Index formulas for geometric Dirac operators in Riemannian foliations ⋮ Bismut superconnections and the Chern character for Dirac operators on foliated manifolds ⋮ Induced cyclic cocycles and higher eta invariants ⋮ Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint. ⋮ Eta cocycles, relative pairings and the Godbillon-Vey index theorem ⋮ \(L^{2}\)-invariants of Riemannian foliations ⋮ Gromov's translation algebras, growth and amenability of operator algebras ⋮ \(L^{2}\)-Lefschetz distribution of Lie foliations ⋮ Remark on a paper of E. Ghys ⋮ Foliation \(C^\ast\)-algebras on multiply fibred manifolds ⋮ Fonctorialité en K-théorie bivariante pour les variétés lipschitziennes. (Functoriality in the bivariant K-theory for Lipschitz manifolds) ⋮ Gradients for \(SL(q)\)-foliations ⋮ A groupoid proof of the Lefschetz fixed point formula ⋮ The longitudinal cocycle and the index of Toeplitz operators ⋮ Hodge decomposition along the leaves of Riemannian foliation ⋮ Transversal Dirac families in Riemannian foliations ⋮ A vanishing result for the \(\mathrm{Spin}^{c}\) Dirac operator defined along the leaves of a foliation ⋮ Dirac operators on foliations with invariant transverse measures

Cites Work

• Foliations, the ergodic theorem and Brownian motion
• The graph of a foliation
• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• On the heat equation and the index theorem
• Essential self-adjointness of powers of generators of hyperbolic equations
• Functional Analysis

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