Supermanifold

Summary

A supermanifold is a space whose functions depend on ordinary commuting coordinates and also on anticommuting coordinates. Formally, it is a topological space with a sheaf of supercommutative superalgebras that looks locally like smooth functions with values in an exterior algebra. Supermanifolds are the geometric setting of supersymmetry, where bosons are described by even and fermions by odd coordinates. Every smooth supermanifold is built, up to isomorphism, from an ordinary vector bundle over an ordinary manifold.