Supermanifolds

Part of speech: noun

Definitions

1. Smooth geometric spaces combining traditional manifold structures with additional algebraic elements capturing supersymmetry and graded variables
2. Mathematical constructs extending classical differentiable manifolds by incorporating both commuting and anticommuting coordinates to model physical theories involving supersymmetry
3. Advanced topological entities that generalize manifolds to include extra dimensions governed by algebraic rules reflecting fermionic and bosonic variables in theoretical physics contexts

Etymology: "Supermanifolds" is the plural of "supermanifold," a compound formed from the prefix "super-" and "manifold." The prefix descends from Latin "super," meaning "above" or "over," which traces back through Proto-Italic to the Proto-Indo-European root "*uper," the same root behind English "over" and "upper." "Manifold" in its mathematical sense refers to a space that locally resembles ordinary Euclidean space, so a supermanifold is a manifold extended with additional, anticommuting coordinates alongside the familiar commuting ones. The word is a plain technical coinage: it combines a familiar prefix with an existing mathematical term, so the "super-" signals the added layer of structure rather than any literal sense of height. Its meaning comes entirely from the physics it serves, where these objects provide a geometric setting for supersymmetry.

Synonyms: supergeometry manifold