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List of geometric topology topics
This is a
list of
geometric topology
topics
.
Low-dimensional topology
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
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-manifolds
Moise's Theorem
(see also
Hauptvermutung
)
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
(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
Invariants
Fundamental group
Heegaard genus
tri-genus
Analytic torsion
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
I-bundle
See also
topology glossary
List of topology topics
List of general topology topics
List of algebraic topology topics
Publications in topology
v
t
e
Topology
Fields
General (point-set)
Algebraic
Combinatorial
Continuum
Differential
Geometric
low-dimensional
Homology
cohomology
Set-theoretic
Digital
Key concepts
Open set
/
Closed set
Interior
Continuity
Space
compact
connected
Hausdorff
metric
uniform
Homotopy
homotopy group
fundamental group
Simplicial complex
CW complex
Polyhedral complex
Manifold
Bundle (mathematics)
Second-countable space
Cobordism
Metrics and properties
Euler characteristic
Betti number
Winding number
Chern number
Orientability
Key results
Banach fixed-point theorem
De Rham cohomology
Invariance of domain
Poincaré conjecture
Tychonoff's theorem
Urysohn's lemma
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