What is a stratifold?

Answer 1

Stratifolds were introduced by Kreck as a generalization of manifolds. Briefly, a stratifold is a pair, consisting of a topological space S together with a subsheaf of the sheaf of continuous real functions on S. S is assumed to be locally compact, Hausdorff and second countable and thus paracompact. The sheaf structure is assumed to present S as a union of strata which are smooth manifolds.

Among the examples of stratifolds are manifolds, real and complex

algebraic varieties, and the one point compactification of a manifold.

The cone over a stratifold and the product of two stratifolds are

again stratifolds.