nLab noncommutative geometry - contents

noncommutative geometry

(geometry $\leftarrow$ Isbell duality $\to$ algebra)

Topology

• noncommutative topology
• C*-algebra, Gelfand duality
• quantale

Smooth and Riemannian geometry

• dense subalgebra

• spectral triple

• 2-spectral triple

Algebraic geometry

• noncommutative algebraic geometry
• noncommutative scheme
• noncommutative motive
• quantum flag variety
• quantum Schubert cell

Homotopy theory

• noncommutative stable homotopy theory

  • model structure on operator algebras

  • homotopical structure on C*-algebras

• KK-theory, E-theory

• cyclic homology

Relation to physics

• deformation quantization

• algebra of observables, local net of observables

• Bohr topos

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