# What is the relationship between a brane, a manifold, and a space?

I've read many ways to define manifold; one way is to define it as a type of mathematical space (a type of topological space to be exact).

All of the definitions that I've seen for brane, on the other hand, don't really classify it as a type of anything.

To me, a brane sounds a lot like a manifold. Could they be the same thing? If not, a brane is surely a topological space, or just generally a mathematical space, right?

• A definition that I know of is that p-branes are D-dimensional manifolds with SO(D-1-p) symmetry. So I would say that branes are a special type of manifold, but I don't know. There might be a more general definition or definitions for different contexts. Dec 24 '15 at 21:50
• I don't think branes would really classify as manifolds in a strict sense. A manifold is a classical geometric/topological construction in mathematics, while a brane is a somewhat vague physical idea that is usually understood as being a quantum mechanical object. Dec 24 '15 at 22:19