This is a list of geometric topology topics.

Low-dimensional topology

Manifolds in general

v t e Topology
Fields	General (point-set) Algebraic Combinatorial Continuum Differential Geometric low-dimensional Homology cohomology Set-theoretic Digital
Key concepts	Open set / Closed set Interior Continuity Space compact connected Hausdorff metric uniform Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism
Metrics and properties	Euler characteristic Betti number Winding number Chern number Orientability
Key results	Banach fixed-point theorem De Rham cohomology Invariance of domain Poincaré conjecture Tychonoff's theorem Urysohn's lemma
Category Mathematics portal Wikibook Wikiversity Topics general algebraic geometric Publications