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

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

noncommutative topology, noncommutative geometry

noncommutative stable homotopy theory

**genus, orientation in generalized cohomology**

By *noncommutative stable homotopy theory* is meant an analog of classical *stable homotopy theory* obtained as one passes from topology to noncommutative topology, hence as one generalizes topological spaces to non-neccesarily commutative (formal duals of) C*-algebras.

The concrete implementation of such *noncommutative stable homotopy theory* is usually taken to be *KK-theory* or rather *E-theory*. See there for details.

A reference that mentions the term “noncommutative stable homotopy theory” explicitly is

- Martin Grensing,
*Noncommutative stable homotopy theory*(arXiv:1302.4751)

Last revised on May 20, 2013 at 12:43:04. See the history of this page for a list of all contributions to it.