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