Analysis on fractals or calculus on fractals is a generalization of calculus on smooth manifolds to calculus on fractals.
Differentiable manifolds (of a given dimension) are all locally diffeomorphic (by definition), so there are no local invariants to a differentiable structure (beyond dimension).
Riemannian manifold | manifold | Manifold | Differentiable manifold | 4-manifold | Stein manifold | Simplicial manifold | Riemann manifold | Piecewise linear manifold | Manifold Trilogy | Leek and Manifold Valley Light Railway | Finsler manifold | E8 manifold | Complex manifold | complex manifold | closed manifold | 3-manifold |