Section
Noncommutative Geometry
Spectral triples, noncommutative metric geometry, cyclic theory, K-homology, and semifinite geometry.
Core idea
Click any term to expand its definition inline.
Noncommutative geometry
Smooth-algebra bridge
Spectral triples
- Almost-commutative spectral triple
- Canonical spectral triple of a compact spin manifold
- Dirac operator
- Dirac-type operator
- Even spectral triple
- Nonunital spectral triple
- Odd spectral triple
- Product of spectral triples
- Spectral triple
- Unitary equivalence of spectral triples
Real structures
- First-order condition for a real spectral triple
- KO-dimension sign table for a real spectral triple
- Order-zero condition for a real spectral triple
- Real spectral triple
- Real structure on a spectral triple
Regularity, summability, and dimension spectrum
- Derivation delta(T)=[|D|,T]
- Dimension spectrum of a spectral triple
- Finitely summable spectral triple
- Metric dimension of a spectral triple
- Noncommutative integral of a spectral triple
- p-summable spectral triple
- Regular spectral triple
- Smooth domain of the Dirac derivation
- Spectral zeta function of a spectral triple
- Theta-summable spectral triple
Metric noncommutative geometry
K-homology and index pairing
- Analytic K-homology
- Bounded transform of a spectral triple
- Even Fredholm module
- Even K-theory/K-homology index pairing
- Fredholm module
- Odd Fredholm module
- Odd K-theory/K-homology index pairing
- p-summable Fredholm module
- Spectral flow
- Unbounded Kasparov module
Cyclic homology and local index machinery
- Chern character of a Fredholm module
- Cyclic cohomology
- Periodic cyclic cohomology
- Entire cyclic cohomology
- Hochschild chain complex
- Hochschild cycle
- Jaffe-Lesniewski-Osterwalder cocycle
- Local index formula in noncommutative geometry
Reconstruction and orientability
- Commutative reconstruction theorem for spectral triples
- Finiteness and absolute-continuity axiom for a spectral triple
- Hochschild orientability axiom for a spectral triple