List Of Geometric Topology Topics

Knot theory

• Knot (mathematics)
• Link (mathematics)
• 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
• Borromean rings
• Hyperbolic link
• Writhe
• Quandle
• Kirby calculus
• Seifert surface

Surfaces

• Genus (mathematics)
• Dehn twist
• Examples
• Positive Euler characteristic
• 2-disk
• Sphere
• Real projective plane
• Zero Euler characteristic
• Annulus
• Mbius 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
• Poincar conjecture
• Thurston elliptization conjecture
• Thurston's Geometrization Conjecture
• Examples
• 3-sphere
• Torus bundles

Manifolds in general

• Orientable manifold
• Connected sum
• Jordan-Schnflies 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

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