nLab 11-manifold

Idea

An 11-manifold is a manifold of dimension 11. (Generally a topological manifold, but it can be specified to a PL manifold or a smooth manifold.) 11-manifolds are of particular interest as underlying spacetime in M-theory and its low energy limit in D=11 supergravity.

Examples

• 11-sphere
• real projective space$\mathbb{R}P^11$

Properties

Proposition

For a smooth 11-manifold $M$, its last three Stiefel-Whitney classes vanish:

$$w_9(M) =w_10(M) =w_11(M) =0.$$

More generally, for every $4n+3$-dimensional smooth manifold, one has $w_{4n+1}=w_{4n+2}(M)=w_{4n+3}(M)=0$. Hence this property also holds for 3-manifolds, 7-manifolds and 15-manifolds.

Related concepts

manifolds in low dimension:

• 2-manifolds

• 3-manifolds

• 4-manifolds

• 5-manifolds

• 6-manifolds

• 7-manifolds

• 8-manifolds

• 9-manifolds

• 10-manifolds

• 11-manifolds

• 12-manifolds

• 13-manifolds

• 14-manifolds

• 15-manifolds

• 16-manifolds

Applications of 11-manifolds:

• D=11 Chern-Simons theory
• D=11 N=1 supergravity
• D=11 supergravity Lie 3-algebra