nLab noncommutative stable homotopy theory

Idea

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.

Related concepts

• homotopical structure on C*-algebras

• index theory

References

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

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

But see at KK-theory and E-theory for more references.