List of geometric topology topics

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This is a list of geometric topology topics.

## Contents

* 1 Low-dimensional topology
* 1.1 Knot theory
* 1.2 Surfaces
* 1.3 Three-manifolds
* 2 Manifolds in general
* 3 See also

## Low-dimensional topology

### Knot theory

See also: List of mathematical knots and links

* Knot (mathematics)
* Link (knot theory)
* Wild knots
* Examples of knots (and links)
* Unknot
* Trefoil knot
* Figure-eight knot (mathematics)
* Borromean rings
* Types of knots (and links)
* Torus knot
* Prime knot
* Alternating knot
* Hyperbolic link
* Knot invariants
* Crossing number
* Linking number
* Skein relation
* Knot polynomials
* Alexander polynomial
* Jones polynomial
* Knot group
* Writhe
* Quandle
* Seifert surface
* Braids
* Braid theory
* Braid group
* Kirby calculus

### Surfaces

* Genus (mathematics)
* Examples
* Positive Euler characteristic
* 2-disk
* Sphere
* Real projective plane
* Zero Euler characteristic
* Annulus
* Möbius strip
* Torus
* Klein bottle
* Negative Euler characteristic
* The boundary of the pretzel is a genus three surface
* Embedded/Immersed in Euclidean space
* Cross-cap
* Boy's surface
* Roman surface
* Steiner surface
* Alexander horned sphere
* Klein bottle
* 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
* 3-sphere
* Torus bundles
* Surface bundles over the circle
* Graph manifolds
* Knot complements
* Whitehead manifold
* Invariants
* Fundamental group
* Heegaard genus
* tri-genus
* Analytic torsion

## Manifolds in general

See also: List of manifolds

* Orientable manifold
* Connected sum
* Jordan-Schönflies theorem
* Signature (topology)
* Handle decomposition
* Handlebody
* h-cobordism theorem
* s-cobordism theorem
* Manifold decomposition
* Hilbert-Smith conjecture
* Mapping class group
* Orbifolds
* Examples
* Exotic sphere
* Homology sphere
* Lens space
* I-bundle

## See also

* topology glossary
* List of topology topics
* List of general topology topics
* List of algebraic topology topics
* Publications in topology

* v
* t
* e

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

* Category
*   * Wikibook
* Wikiversity
* Topics
* general
* algebraic
* geometric
* Publications

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