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)