nmen

nmen is a term used in speculative discussions of geometry to denote a hypothetical class of objects that generalize ordinary n-dimensional manifolds by incorporating extra local data. An nmen consists of a topological space M of dimension n together with an auxiliary local structure defined on charts and compatible on overlaps.

The added data can take several forms, such as a sheaf, a group action, or a system of local invariants. In the simplest interpretation, the extra data is trivial, and every ordinary n-manifold is an nmen. Nontrivial data may influence global properties without altering the underlying topology.

Variants of nmen are used in pedagogy to illustrate how local refinements interact with global geometry. Examples include decorated or colored n-manifolds, or orbifold-like objects where the local structure encodes symmetry.

Despite these illustrations, nmen is not a standard object in mainstream mathematics and appears mainly in expository or speculative contexts. It serves as a conceptual tool rather than a canonical research subject.

See also: manifold, n-manifold, orbifold, sheaf.