Spectral flow, eta invariants, and von Neumann algebras

DOI10.1016/0022-1236(92)90022-BzbMath0783.57015OpenAlexW1992428069MaRDI QIDQ1803327

Varghese Mathai

Publication date: 29 June 1993

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

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90022-b

zbMATH Keywords

representationsfundamental groupspectral flow\(\eta\)-invarianthomotopy invariant

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Applications of global analysis to structures on manifolds (57R57)

Related Items

Noncommutative knot theory, The Hochschild class of the Chern character for semifinite spectral triples, Examples of odd index theorems, Von Neumann algebra invariants of Dirac operators, Spectral sections, twisted rho invariants and positive scalar curvature, Positive scalar curvature metrics via end-periodic manifolds, On Invariants of Hirzebruch and Cheeger-Gromov, Leafwise homotopies and Hilbert-Poincaré complexes. I: Regular HP-complexes and leafwise pull-back maps, The Higson-Roe exact sequence and \(\ell^2\) eta invariants, The local index formula in semifinite von Neumann algebras. I: Spectral flow, Jumps of the eta-invariant. (With an appendix by Shmuel Weinberger: Rationality of \(\rho\)-invariants), Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators, Two-torsion in the grope and solvable filtrations of knots

Cites Work

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• The index of elliptic operators. III
• Novikov's higher signature and families of elliptic operators
• Homotopy invariance of η-invariants
• On the Analytic Torsion and Eta Invariant for Negatively Curved Manifolds
• Spectral asymmetry and Riemannian geometry. III