List of geometric topology topics

This is a list of geometric topology topics.

Knot theory

 * Knot (mathematics)
 * Link (knot theory)
 * Wild knots
 * Examples of knots
 * Unknot
 * Trefoil knot
 * Figure-eight knot (mathematics)
 * 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

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