noncommutative topology, noncommutative geometry

noncommutative stable homotopy theory

**genus, orientation in generalized cohomology**

**spin geometry**, **string geometry**, **fivebrane geometry** …

**rotation groups in low dimensions**:

see also

The index of a Dirac operator. fiber integration in K-theory

(…)

(…)

Chapter III of

- H. Blaine Lawson, Marie-Louise Michelsohn,
*Spin geometry*, Princeton University Press (1989)

Introductions include

- Troels Roussau Johansen,
*Introduction to the index theory of Dirac operators*(pdf)

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