Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data). It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics.
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Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data). It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics.
has abstract
En mathématiques, et plus préc ...... cations en physique théorique.
@fr
Il teorema di Atiyah-Singer so ...... o la medaglia Fields nel 1990.
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In de differentiaalmeetkunde, ...... n de theoretische natuurkunde.
@nl
In differential geometry, the ...... ations to theoretical physics.
@en
Na geometria diferencial, o te ...... iyah e Isadore Singer em 1963.
@pt
Στη διαφορική γεωμετρία το Θεώ ...... φαρμογές στη Θεωρητική φυσική.
@el
В диференційній геометрії, тео ...... осування в теоретичній фізиці.
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Теорема Атьи — Зингера об инде ...... ельное направление -теории — .
@ru
في علم الهندسة التفاضلية، هناك ...... ة تطبيقات في الفيزياء النظرية.
@ar
アティヤ=シンガーの指数定理(Atiyah–Singer i ...... から、アティヤとシンガーは2004年にアーベル賞を受賞した。
@ja
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author1-link
Michael Atiyah
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Simon Donaldson
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author2-link
Isadore Singer
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Raoul Bott
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author3-link
Vijay Kumar Patodi
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authorlink
Alain Connes
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Dennis Sullivan
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Edward Witten
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Ezra Getzler
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Isadore Singer
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Israel Gelfand
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Michael Atiyah
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consequences
first
Alain
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Dennis
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Edward
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Ezra
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Henri
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Isadore M.
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Isadore
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Israel
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M.A.
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M.I.
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first proof by
Michael Atiyah and Isadore Singer
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first proof date
id
I/i050650
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last
Atiyah
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Bott
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Connes
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Donaldson
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Gel'fand
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Getzler
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Moscovici
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Patodi
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Shubin
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Singer
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name
Atiyah–Singer index theorem
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title
Index formulas
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txt
yes
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wikiPageUsesTemplate
year
subject
comment
En mathématiques, et plus préc ...... cations en physique théorique.
@fr
Il teorema di Atiyah-Singer so ...... alla K-teoria sviluppata dall
@it
In de differentiaalmeetkunde, ...... n de theoretische natuurkunde.
@nl
In differential geometry, the ...... ations to theoretical physics.
@en
Na geometria diferencial, o te ...... iyah e Isadore Singer em 1963.
@pt
Στη διαφορική γεωμετρία το Θεώ ...... φαρμογές στη Θεωρητική φυσική.
@el
В диференційній геометрії, тео ...... осування в теоретичній фізиці.
@uk
Теорема Атьи — Зингера об инде ...... ельное направление -теории — .
@ru
في علم الهندسة التفاضلية، هناك ...... ة تطبيقات في الفيزياء النظرية.
@ar
アティヤ=シンガーの指数定理(Atiyah–Singer i ...... から、アティヤとシンガーは2004年にアーベル賞を受賞した。
@ja
label
Atiyah-Singer-Indexsatz
@de
Atiyah–Singer index theorem
@en
Indexstelling van Atiyah-Singer
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Teorema di Atiyah-Singer
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Teorema do índice de Atiyah-Singer
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Théorème de l'indice d'Atiyah-Singer
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Θεώρημα δείκτη Ατίγια-Σίνγκερ
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Теорема Атьи — Зингера об индексе
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Теорема Атії — Зінгера про індекс
@uk
نظرية أس عطية-سينجر
@ar