High Quality Content by WIKIPEDIA articles! In physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use, some of which are described below. This is different from the alternative definition where, using a fixed Grassmann algebra generated by a countable number of generators ?, one defines a supermanifold as a point set space using charts with the "even coordinates" taking values in the linear combination of elements of ? with even grading and the "odd coordinates" taking values which are linear combinations of elements of ? with odd grading. This raises the question of the physical meaning of all these Grassmann-valued variables. Many physicists claim that they have none and that they are purely formal; if this is the case, this may make the definition in the main part of the article more preferable.

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