List of geometric topology topics

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

Knot theory

See also List of mathematical knots and links

• Prime knot
• Alternating knot
• Knot invariants
  • Crossing number
  • Linking number
  • Skein relation
  • Knot polynomials
    • Alexander polynomial
    • Jones polynomial
• Knot group
• Braids
  • Braid theory
  • Braid group
• Examples of knots
  • Unknot
  • Trefoil knot
  • Figure-eight knot (mathematics)
  • Torus knot
• link (mathematics)
  • Borromean rings
  • Hyperbolic link
• Loop (knot)
  • List of loop knots
• Writhe
• Quandle
• Kirby calculus

Surfaces

• Genus (mathematics)
• Dehn twist
• 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

Three-manifolds

• Heegaard splittings
• Incompressible surface
• Compression body
• Haken manifold
• JSJ decomposition
• Poincaré conjecture
  • Thurston elliptization conjecture
  • Thurston's Geometrization Conjecture
• Examples
  • Three-sphere
  • Torus bundles

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
• Exotic sphere
• Hilbert-Smith conjecture
• Mapping class group
• Examples
  • Homology sphere
  • Lens space