The eta invariant for even dimensional \(PIN_ c\) manifolds

DOI10.1016/0001-8708(85)90119-7zbMath0602.58041OpenAlexW2035667065MaRDI QIDQ1081939

Peter B. Gilkey

Publication date: 1985

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(85)90119-7

zbMATH Keywords

eta invariantK-theoryindex theory

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Index theory and related fixed-point theorems on manifolds (58J20) Differential complexes (58J10) Topological (K)-theory (55N15)

Related Items (14)

Unnamed Item ⋮ Time reversal, \(\mathrm{SU}(N)\) Yang-Mills and cobordisms: Interacting topological superconductors/insulators and quantum spin liquids in 3+1D ⋮ Exotic structures on 4-manifolds detected by spectral invariants ⋮ The index of Callias-type operators with Atiyah-Patodi-Singer boundary conditions ⋮ Smooth structures on nonorientable four-manifolds and free involutions ⋮ A mod 2 index theorem for \(\mathrm{pin}^-\) manifolds ⋮ The eta invariant and parity conditions. ⋮ The Atiyah–Singer index theorem ⋮ Unnamed Item ⋮ Eta and rho invariants on manifolds with edges ⋮ Exotic involutions of low-dimensional spheres and the eta-invariant ⋮ Positive scalar curvature, diffeomorphisms and the Seiberg-Witten invariants ⋮ Stability theorems for chiral bag boundary conditions ⋮ Circle bundles, adiabatic limits of \(\eta\)-invariants and Rokhlin congruences

Cites Work

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• The eta invariant and the K-theory of odd dimensional spherical space forms
• Invariants of the heat equation
• The residue of the global eta function at the origin
• Spectral asymmetry and zeta functions
• Spectrum and the fixed point sets of isometries. II
• The residue of the local eta function at the origin
• Harmonic spinors
• Clifford modules
• The eta invariant for a class of elliptic boundary value problems
• Spectral asymmetry and Riemannian Geometry. I
• Spectral asymmetry and Riemannian geometry. II
• Spectral asymmetry and Riemannian geometry. III
• The fixed point theorem of atiyah‐bott via parabolic operators
• Vector fields on spheres

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