List of geometric topology topics

From Wikipedia, the free encyclopedia

This is a list of geometric topology topics, by Wikipedia page.

Contents 1 Low-dimensional topology 1.1 Knot theory 1.2 Surfaces 1.3 Three-manifolds 2 Manifolds in general

[edit] Low-dimensional topology

[edit] Knot theory

See also List of mathematical knots and links

• 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

[edit] 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

[edit] Three-manifolds

• Moise's Theorem (see also Hauptvermutung)
• Poincaré conjecture
  • Thurston elliptization conjecture
• Seifert fiber space
• Hyperbolic 3-manifold
  • Thurston's geometrization conjecture
• 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

[edit] Manifolds in general

See also List of manifolds

• 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