# nLab exceptional geometry

### Context

#### Riemannian geometry

Riemannian geometry

# Contents

## Idea

The classification of Riemannian manifolds with special holonomy contains two “exceptional” cases: G2-holonomy in dimension 7, and Spin(7)-holonomy in dimension 8. Their study is the topic of exceptional geometry.

Sometimes more generally, exceptional geometry is understod to study spaces controled by exceptional Lie groups in some way.

## References

### General

General discussion is in

Discussion of G2 manifolds is in

• Spiro Karigiannis, $G_2$-manifolds – Exceptional structures in geometry arising from exceptional algebra (pdf)

### In supergravity

Applications to supergravity are discussed in

For more along these lines see the references at exceptional generalized geometry.

Revised on February 7, 2012 22:00:04 by Urs Schreiber (89.204.130.102)