This is a list of geometric topology topics.
Low-dimensional topology
Knot theory
- Knot (mathematics)
- Link (knot theory)
- Wild knots
- Examples of knots
- Types of knots
- Knot invariants
- Writhe
- Quandle
- Seifert surface
- Braids
- Kirby calculus
Surfaces
- Genus (mathematics)
- Examples
- Positive Euler characteristic
- Zero Euler characteristic
- Negative Euler characteristic
- The boundary of the pretzel is a genus three surface
- Embedded/Immersed in Euclidean space
- Mapping class group
Three-manifolds
- Moise's Theorem (see also Hauptvermutung)
- Poincaré 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
See also
- topology glossary
- List of topology topics
- List of general topology topics
- List of algebraic topology topics
- Publications in topology
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