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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?

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    $\begingroup$ 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. $\endgroup$ Dec 24 '15 at 21:50
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    $\begingroup$ 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. $\endgroup$
    – CuriousOne
    Dec 24 '15 at 22:19
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A brane is more than just a manifold, it is a physical object. You can think of it as a higher dimensional version of a particle. It can carry a charge, it can couple to gauge fields, it can decay, etc. We tend to study a brane in the same way we study a string. We study strings in terms of their worldsheet, we study branes in terms of their worldvolume. The worldvolume of a brane is a manifold.

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