orbifoldlike

Orbifoldlike is an informal mathematical descriptor used to indicate that a space or object shares structural features with orbifolds without necessarily satisfying all formal orbifold axioms. In typical usage, a space is orbifoldlike if every point has a neighborhood that is locally modeled on a quotient R^n by a finite group G acting linearly, and if these local models can be assembled in a manner reminiscent of an orbifold atlas. The term thus emphasizes local structure and singularities rather than a guaranteed global quotient presentation.

Because the term is informal, precise meaning varies by author. Some require only local quotient structure with finite isotropy groups, while others demand a more systematic collection of charts with compatibility conditions akin to an orbifold atlas but with potential relaxations. The resulting singular set consists of points with nontrivial isotropy, and in low dimensions these singularities often resemble classical quotient singularities.

Orbifoldlike spaces frequently occur as quotients of manifolds by finite group actions, as underlying spaces of certain moduli spaces with finite automorphism groups, or as local models in the study of stacky or V-manifold structures. They can serve as a bridge to true orbifolds in contexts where a full orbifold structure is not yet established or not required.

See also: orbifold, quotient singularity, V-manifold, stack, group action.