List of geometric topology topics

Table of contents

1 Surfaces 2 Knot theory 3 Manifolds

Surfaces

• Genus (mathematics)
• Klein bottle
• Real projective plane
  • Boy's surface
  • Roman surface
  • Steiner surface
• Möbius strip
  • Cross-cap
• Sphere
• Torus
• Pretzel

• Unknot
• Prime knot
• Crossing number
• Loop (knot)
• List of loop knots
• Figure-eight knot (mathematics)
• Trefoil knot
• Linking number
• Knot invariant
• Knot polynomial
  • Alexander polynomial
  • Jones polynomial
  • Skein relation
• Braid theory
  • Braid group

• Orientable manifold
• Connected sum
• Jordan-Schönflies theorem
• Alexander horned sphere
• Homology sphere
• Torus bundle
• h-cobordism theorem
• s-cobordism theorem
• Haken manifold
• Jaco-Shalen-Johannson torus decomposition
• Poincaré conjecture
  • Thurston elliptization conjecture
  • Thurston's Geometrization Conjecture
• Hilbert-Smith conjecture