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In mathematics, low-dimensional topology is the branch of topology that studies manifolds of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. It can be regarded as a part of geometric topology.

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  • Low-dimensional topology
  • Topologia in dimensione bassa
  • Topologie en basses dimensions
  • 低次元トポロジー
  • Laag-dimensionale topologie
  • Topologia de baixa dimensão
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  • In mathematics, low-dimensional topology is the branch of topology that studies manifolds of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. It can be regarded as a part of geometric topology.
  • 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 ou 4 (en) et la théorie des nœuds et des tresses. Elle fait partie de la topologie géométrique.
  • 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.
  • 数学において、低次元トポロジー(low-dimensional topology)は、トポロジーの一分野で、4次元、あるいはそれ以下の次元の多様体の研究をする。低次元トポロジーで扱われるトピックは、3次元多様体(3-manifold)や 4次元多様体の構造論、結び目理論、ブレイド群などがある。低次元トポロジーは幾何学的トポロジーの一部と見なすことができる。
  • 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.
  • 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 structuur theorie van 3- en 4-variëteiten, knopentheorie en vlechtgroepen. Het wordt als een onderdeel van de meetkundige topologie beschouwd.
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