List of geometric topology topics

This is a list of geometric topology topics, by Wikipedia page. See also:

Low-dimensional topology

Knot theory

Surfaces

Genus (mathematics)
Examples
- Positive Euler characteristic
  - 2-disk
  - Sphere
  - Real projective plane
- Zero Euler characteristic
- Negative Euler characteristic
  - The boundary of the pretzel is a genus three surface
- Embedded/Immersed in Euclidean space
Mapping class group
- Dehn twist
- Nielsen–Thurston classification

Three-manifolds

Moise's Theorem (see also Hauptvermutung)
Poincaré conjecture
- Thurston elliptization conjecture
Thurston's geometrization conjecture
- Hyperbolic 3-manifolds
- Spherical 3-manifolds
- Euclidean 3-manifolds, Bieberbach Theorem, Flat manifolds, Crystallographic groups
- Seifert fiber space
Heegaard splitting
- Waldhausen conjecture
- Compression body
- Handlebody
Incompressible surface
- Dehn's lemma
- Loop theorem (aka the Disk theorem)
- Sphere theorem
Haken manifold
JSJ decomposition
Branched surface
Lamination
Examples
Invariants

Manifolds in general

Topology
Fields	General (point-set) Algebraic Combinatorial Continuum Differential Geometric low-dimensional Homology cohomology Set-theoretic
Key concepts	Open set / Closed set Continuity Space compact Hausdorff metric uniform Homotopy homotopy group fundamental group Simplicial complex CW complex Manifold Second-countable space
Category Mathematics portal Wikibook Wikiversity Topics general algebraic geometric Publications

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