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In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space.

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  • Abbildungsklassengruppe
  • Mapping class group
  • Mapping class group
  • 사상류군
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  • In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space.
  • In matematica, e più precisamente in topologia, il mapping class group (letteralmente, gruppo delle classi di applicazioni) è un importante invariante algebrico di uno spazio topologico. Detto brevemente, è un di "simmetrie" dello spazio.
  • 위상수학에서, 사상류군(寫像類群, 영어: mapping class group)은 어떤 위상 공간의 자기 위상 동형들의 호모토피류들로 구성된 군이다.
  • Die Abbildungsklassengruppe eines Raumes ist die Gruppe der „Symmetrien“ (Klassen von Abbildungen) dieses Raumes. Dabei werden Abbildungen, die sich stetig ineinander deformieren lassen, als jeweils eine Klasse von Abbildungen angesehen. , wobei die kompakt-offene Topologie trägt und die -te Homotopiemenge (also die Menge der Wegzusammenhangskomponenten) bezeichnet. Meist, insbesondere in gruppentheoretischem Kontext, sind Abbildungsklassengruppen von orientierbaren Flächen gemeint, wenn von „Abbildungsklassengruppen“ die Rede ist.
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