| dbo:abstract |
In mathematics, in particular in partial differential equations and differential geometry, an elliptic complex generalizes the notion of an elliptic operator to sequences. Elliptic complexes isolate those features common to the de Rham complex and the Dolbeault complex which are essential for performing Hodge theory. They also arise in connection with the Atiyah-Singer index theorem and Atiyah-Bott fixed point theorem. (en) 편미분 방정식 이론과 미분기하학에서 타원 복합체(楕圓複合體, elliptic complex)란 프레드홀름 작용소로 이루어진 사슬 복합체다. 드람 복합체와 돌보 복합체를 일반화한 것이다. (ko) 数学の、特に偏微分方程式や微分幾何学における楕円型複体（だえんがたふくたい、英: elliptic complex）とは、楕円型作用素の概念を列に一般化したものである。楕円型複体は、ホッジ理論を展開する上で本質的となるド・ラーム複体とドルボー複体に共通の特徴を取り出したものである。アティヤ＝シンガーの指数定理とアティヤ＝ボットの不動点定理の関連でも現れる。 (ja) |
| dbo:wikiPageExternalLink |
https://www.jstor.org/stable/1970715%7Cjournal=The |
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3189496 (xsd:integer) |
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2012 (xsd:nonNegativeInteger) |
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dbt:Cite_journal dbt:Differential-geometry-stub |
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dbc:Differential_geometry dbc:Elliptic_partial_differential_equations |
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| rdfs:comment |
In mathematics, in particular in partial differential equations and differential geometry, an elliptic complex generalizes the notion of an elliptic operator to sequences. Elliptic complexes isolate those features common to the de Rham complex and the Dolbeault complex which are essential for performing Hodge theory. They also arise in connection with the Atiyah-Singer index theorem and Atiyah-Bott fixed point theorem. (en) 편미분 방정식 이론과 미분기하학에서 타원 복합체(楕圓複合體, elliptic complex)란 프레드홀름 작용소로 이루어진 사슬 복합체다. 드람 복합체와 돌보 복합체를 일반화한 것이다. (ko) 数学の、特に偏微分方程式や微分幾何学における楕円型複体（だえんがたふくたい、英: elliptic complex）とは、楕円型作用素の概念を列に一般化したものである。楕円型複体は、ホッジ理論を展開する上で本質的となるド・ラーム複体とドルボー複体に共通の特徴を取り出したものである。アティヤ＝シンガーの指数定理とアティヤ＝ボットの不動点定理の関連でも現れる。 (ja) |
| rdfs:label |
Elliptic complex (en) 楕円型複体 (ja) 타원 복합체 (ko) |
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freebase:Elliptic complex yago-res:Elliptic complex wikidata:Elliptic complex dbpedia-ja:Elliptic complex dbpedia-ko:Elliptic complex https://global.dbpedia.org/id/4jQjG |
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