Spectral asymmetry and zeta functions

DOI10.1007/BF01404760zbMath0489.58030OpenAlexW2060255161MaRDI QIDQ1166814

Mariusz Wodzicki

Publication date: 1982

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142873

zbMATH Keywords

micro-local analysismeromorphic extensions of eta functionself-adjoint elliptic pseudo- differential operator space of smooth sections smooth bundle over compact Riemannian manifold without boundaryvanishing of residues of zeta- function

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Exotic index theories on manifolds (58J22) Integral, integro-differential, and pseudodifferential operators (47Gxx)

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Complex powers of elliptic pseudodifferential operators ⋮ Desuspension of splitting elliptic symbols. I ⋮ The eta invariant for even dimensional \(PIN_ c\) manifolds ⋮ Wavetrace asymptotics for operators of dirac type ⋮ Spectral functions of subordinate Brownian motion on closed manifolds: ⋮ The Residue Determinant ⋮ A groupoid approach to the Wodzicki residue ⋮ Periodicity and the determinant bundle ⋮ Residues of the eta function for an operator of Dirac type ⋮ The regularity of the \(\eta \) function for the Shubin calculus ⋮ A coefficient of an asymptotic expansion of logarithms of determinants for classical elliptic pseudodifferential operators with parameters ⋮ On the topology of the space of invertible pseudodifferential operators of order 0 ⋮ A new proof of the local regularity of the eta invariant of a Dirac operator ⋮ Noncommutative residue and canonical trace on noncommutative tori. Uniqueness results ⋮ SPECTRAL ASYMMETRY, ZETA FUNCTIONS, AND THE NONCOMMUTATIVE RESIDUE ⋮ Local invariants of spectral asymmetry

Cites Work

• Unnamed Item
• Closed geodesics and the \(\eta\)-invariant
• The residue of the local eta function at the origin
• Spectral Asymmetry and Riemannian Geometry
• Spectral asymmetry and Riemannian Geometry. I
• Spectral Geometry and Invariants from Differential Topology
• Spectral asymmetry and Riemannian geometry. II
• Spectral asymmetry and Riemannian geometry. III