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

• noncommutative quantum field theory?

• noncommutative open string theory

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