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