| dbo:abstract |
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) |
| dbo:wikiPageExternalLink |
https://web.archive.org/web/20180519183342/http:/math.ucr.edu/home/baez/qg-winter2007/Oxford.pdf http://math.ucr.edu/home/baez/esi/%7Cyear=2007 http://math.ucr.edu/home/baez/qg-winter2007/Oxford.pdf |
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dbr:Cambridge_University_Press dbr:N-group_(category_theory) dbr:Lie_group dbc:Differential_geometry dbc:Group_theory dbc:String_theory dbr:Mathematics dbr:Elliptic_cohomology dbr:Classifying_space dbr:Mathematische_Annalen dbr:Spin_group dbr:2-group dbr:Topological_group dbr:Topology dbr:Frame_bundle dbr:Gerbe dbc:Homotopy_theory dbr:Eilenberg–MacLane_space dbr:Holonomy dbr:Homotopy_fiber dbr:Homotopy_group dbr:Manifold dbr:Bundle_gerbe dbr:Groupoid dbr:Orthogonal_group dbr:Exact_sequence dbr:Whitehead_tower dbr:Higher_group dbr:Postnikov_tower dbr:Arxiv:math/0504123v2 dbr:String_bordism |
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Whitehead+tower (en) string+group (en) |
| dbp:title |
Whitehead tower (en) string group (en) |
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dbt:Citation dbt:Harvtxt dbt:Nlab dbt:Reflist |
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dbc:Differential_geometry dbc:Group_theory dbc:String_theory dbc:Homotopy_theory |
| rdfs:comment |
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) |
| rdfs:label |
끈 군 (ko) String group (en) |
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freebase:String group wikidata:String group dbpedia-ko:String group https://global.dbpedia.org/id/4vYFY |
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wikipedia-en:String_group?oldid=1122210699&ns=0 |
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wikipedia-en:String_group |
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