• 1 Spectral triples ▶
    • 1.1 Odd spectral triples
    • 1.2 Even spectral triples
    • 1.3 Resolvents and finitely summable spectral triples
  • 2 The Fredholm index pairing ▶
    • 2.1 Fredholm operators ▶
      • 2.1.1 Compact perturbations of the identity
    • 2.2 The graded-kernel index
    • 2.3 The general index pairing
  • 3 Examples ▶
    • 3.1 Block-diagonal operators on \(\ell ^2\)
    • 3.2 The Dirac triple of the circle \(S^1\)
    • 3.3 The Dirac triple of the two-torus \(T^2\)
    • 3.4 The unilateral shift on \(\ell ^2(\mathbb {N})\)
    • 3.5 The flux-\(k\) magnetic Dirac model
    • 3.6 Theta sections on the square torus
    • 3.7 The Fourier-coefficient recursion: an exact dimension count
    • 3.8 The Hermite functions: Gaussian-weighted orthogonality
  • Dependency graph

Spectral Triples and the Index Pairing

Jon Bannon and Michael R. Douglas

  • 1 Spectral triples
    • 1.1 Odd spectral triples
    • 1.2 Even spectral triples
    • 1.3 Resolvents and finitely summable spectral triples
  • 2 The Fredholm index pairing
    • 2.1 Fredholm operators
      • 2.1.1 Compact perturbations of the identity
    • 2.2 The graded-kernel index
    • 2.3 The general index pairing
  • 3 Examples
    • 3.1 Block-diagonal operators on \(\ell ^2\)
    • 3.2 The Dirac triple of the circle \(S^1\)
    • 3.3 The Dirac triple of the two-torus \(T^2\)
    • 3.4 The unilateral shift on \(\ell ^2(\mathbb {N})\)
    • 3.5 The flux-\(k\) magnetic Dirac model
    • 3.6 Theta sections on the square torus
    • 3.7 The Fourier-coefficient recursion: an exact dimension count
    • 3.8 The Hermite functions: Gaussian-weighted orthogonality