nLab exceptional tangent bundle

Idea

A generalization of the notion of tangent bundle in exceptional generalized geometry.

For 11-dimensional supergravity the bosonic body of its typical fiber is

$$\mathbb{R}^{d-1,1} \oplus \wedge^2 (\mathbb{R}^{d-1,1})^\ast \oplus \wedge^5 (\mathbb{R}^{d-1,1})^\ast$$

where the second summand corresponds to M2-brane charges and the third to M5-brane charges.

This happens to coincide with the bosonic body of the M-theory super Lie algebra, see there for more.

Related concepts

• generalized tangent bundle

(…)