List of geometric topology topics

This is a list of geometric topology topics.

Low-dimensional topology

Knot theory

• 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

• 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