List of geometric topology topics

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

  [Low-dimensional topology]

[Knot theory]

• Knot
• Link
• Wild knots
• Examples of knots
• *Unknot
• *Trefoil knot
• *Figure-eight knot
• *Borromean rings
• Types of knots
• *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

  Surface">Surface (topology)">Surfaces

• Genus
• 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-manifold">3-manifold">Three-manifolds

• Moise's Theorem
• 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
• *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

  [Manifold]s in general

• Orientable manifold
• Connected sum
• Jordan-Schönflies theorem
• Signature
• 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