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
- *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
Surface">Surface (topology)">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-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