About: Low-dimensional topology

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In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded as a part of geometric topology. It may also be used to refer to the study of topological spaces of dimension 1, though this is more typically considered part of continuum theory.

Attributes	Values
rdf:type	organisation
rdfs:label	Low-dimensional topology (en) Niedrigdimensionale Topologie (de) Topologia in dimensione bassa (it) Topologie en basses dimensions (fr) 低次元トポロジー (ja) Laag-dimensionale topologie (nl) Topologia de baixa dimensão (pt) 低維拓撲 (zh)
rdfs:comment	In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded as a part of geometric topology. It may also be used to refer to the study of topological spaces of dimension 1, though this is more typically considered part of continuum theory. (en) En mathématiques, la topologie en basses dimensions est la branche de la topologie qui concerne les variétés de dimension inférieure ou égale à quatre. Des sujets représentatifs en sont l'étude des variétés de dimension 3 (en) et la théorie des nœuds et des tresses. Elle fait partie de la topologie géométrique. (fr) 数学における低次元位相幾何学（ていじげんいそうきかがく、英: low-dimensional topologyは、4次元、あるいはそれ以下の次元の多様体の研究をする位相幾何学の一分野である。扱われる主題は、および4次元多様体の構造論、結び目理論および組み紐群などがある。低次元トポロジーは幾何学的位相幾何学の一部と見なすことができる。 (ja) A topologia de baixa dimensão, ou topologia geométrica, é a área da topologia dedicada ao estudo das variedades de dimensão inferior ou igual a 4. Inclui a teoria dos nós. O problema mais famoso desta área é a Conjectura de Poincaré. (pt) 在数学中，低维拓扑是拓扑学中研究二、三、四维流形或更广义的拓扑空间的一个分支。有代表性的研究主题包括三维流形、、扭结和辫群等的结构理论。低维拓扑是几何拓扑学的一部分。 (zh) La topologia in dimensione bassa è una branca della topologia (e quindi della geometria) che studia gli "spazi di dimensione 1, 2, 3 e 4". La topologia in dimensione bassa studia soprattutto le varietà, da molteplici punti di vista. A partire dagli anni sessanta, è emersa sempre più la peculiarità di queste dimensioni, il cui studio necessita di strumenti ad hoc, più specifici delle tecniche generali fornite dalla topologia algebrica e della topologia differenziale. Da cui la nascita negli anni 60/70 di un settore apposito, che studiasse tecniche adeguate, soprattutto alle dimensioni 3 e 4. (it) De laag-dimensionale topologie is in de wiskunde een tak van de topologie die variëteiten van vier of minder dimensies bestudeert. Representatieve onderwerpen zijn de structuurtheorie van 3-variëteiten, 4-variëteiten, knopentheorie en vlechtgroepen. Het wordt als een onderdeel van de meetkundige topologie beschouwd. (nl)
foaf:depiction
dcterms:subject	Geometric topology Low-dimensional topology
Wikipage page ID	621774 (xsd:integer)
Wikipage revision ID	1043825652 (xsd:integer)
Link from a Wikipage to another Wikipage	Cardinality of the continuum Presentation of a group Properly discontinuous action Pseudo-Riemannian Robion Kirby Euclidean 3-space Braid group Homeomorphic René Thom Ricci flow Richard S. Hamilton Riemann surface Characteristic class Vaughan Jones List of geometric topology topics Robert Gompf Complement (set theory) Complete space Complex number Complex plane Mathematics Max Dehn Gauge theory Geometric analysis Geometric group theory Geometric topology Neighbourhood (mathematics) Smooth structure Solid torus Tangent bundle Circle Clifford Taubes General Relativity Geometrization conjecture Geometry Braid Braid theory Configuration space (mathematics) Conformal equivalence Connected sum Constant curvature Theory Andrew Casson Simon Donaldson Singularity theory Stephen Smale Closed manifold Complex manifold Embedding Fundamental group Haken manifold Surface (topology) Mathematical physics Ball (mathematics) Topology Torus W. B. R. Lickorish William Thurston Heegaard splitting Jones polynomial 3-sphere 4-sphere 3-manifold Ambient isotopy Euclidean space Exotic R4 Exotic sphere Number theory Partial differential equations Diffeomorphism Floer homology Knot complement Knot theory Riemannian metric Geometric topology Grigori Perelman Group (mathematics) Hyperbolic 3-manifold Hyperbolic geometry

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