In topology, a branch of mathematics, a string group is an infinite-dimensional group introduced by as a -connected cover of a spin group. A string manifold is a manifold with a lifting of its frame bundle to a string group bundle. This means that in addition to being able to define holonomy along paths, one can also define holonomies for surfaces going between strings. There is a short exact sequence of topological groups
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| - 끈 군 (ko)
- String group (en)
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| - 대수적 위상수학과 이론물리학에서 끈 군(-群, 영어: string group)은 스핀 군과 유사하지만, 3차 호모토피 군이 자명한 위상군이다. 이는 유한 차원 리 군으로 표현될 수 없으나, 무한 차원 으로 존재한다. 이에 대응하는 리 대수는 유한 차원의 L∞-대수로 여길 수 있다. (ko)
- In topology, a branch of mathematics, a string group is an infinite-dimensional group introduced by as a -connected cover of a spin group. A string manifold is a manifold with a lifting of its frame bundle to a string group bundle. This means that in addition to being able to define holonomy along paths, one can also define holonomies for surfaces going between strings. There is a short exact sequence of topological groups (en)
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| - Whitehead+tower (en)
- string+group (en)
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| - Whitehead tower (en)
- string group (en)
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| - In topology, a branch of mathematics, a string group is an infinite-dimensional group introduced by as a -connected cover of a spin group. A string manifold is a manifold with a lifting of its frame bundle to a string group bundle. This means that in addition to being able to define holonomy along paths, one can also define holonomies for surfaces going between strings. There is a short exact sequence of topological groups where is an Eilenberg–MacLane space and is a spin group. The string group is an entry in the Whitehead tower (dual to the notion of Postnikov tower) for the orthogonal group: It is obtained by killing the homotopy group for , in the same way that is obtained from by killing . The resulting manifold cannot be any finite-dimensional Lie group, since all finite-dimensional compact Lie groups have a non-vanishing . The fivebrane group follows, by killing . More generally, the construction of the Postnikov tower via short exact sequences starting with Eilenberg–MacLane spaces can be applied to any Lie group G, giving the string group String(G). (en)
- 대수적 위상수학과 이론물리학에서 끈 군(-群, 영어: string group)은 스핀 군과 유사하지만, 3차 호모토피 군이 자명한 위상군이다. 이는 유한 차원 리 군으로 표현될 수 없으나, 무한 차원 으로 존재한다. 이에 대응하는 리 대수는 유한 차원의 L∞-대수로 여길 수 있다. (ko)
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