Atiyah–Singer index theorem

Atiyah–Singer index theorem - theorem that the difference between the dimensions of the kernel and cokernel of a differential operator on a manifold is the integral of a characteristic class. Article "Atiyah–Singer index theorem" in English Wikipedia has 53.2 points for quality (as of November 1, 2023). The article contains 32 references and 25 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that language version.

Since the creation of article "Atiyah–Singer index theorem", its content was written by 107 registered users of English Wikipedia and edited by 281 registered Wikipedia users in all languages.

The article is cited 721 times in English Wikipedia and cited 976 times in all languages.

The highest Authors Interest rank from 2001:

• Local (English): #6250 in September 2003
• Global: #14445 in September 2003

The highest popularity rank from 2008:

• Local (English): #51305 in October 2023
• Global: #93281 in October 2023

There are 20 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from November 1, 2023 (including revision history and pageviews for previous years).

下表顯示了最高品質的文章的語言版本。

#	Language	Quality grade	Quality score
1	English (en) Atiyah–Singer index theorem		53.2149
2	Basque (eu) Atiyah-Singer indizearen teorema		42.7882
3	Catalan (ca) Teorema de l'índex d'Atiyah-Singer		38.3844
4	Spanish (es) Teorema del índice de Atiyah-Singer		36.8166
5	German (de) Atiyah-Singer-Indexsatz		36.0151
6	Chinese (zh) 阿蒂亞-辛格指標定理		30.1345
7	Korean (ko) 아티야-싱어 지표 정리		28.2088
8	Serbian (sr) Ati–Zingerova indeksna teorema		27.1715
9	Persian (fa) قضیه اندیس عطیه-سینگر		25.3413
10	Greek (el) Θεώρημα δείκτη Ατίγια-Σίνγκερ		24.7685

More...

The following table shows the most popular language versions of the article.

The most popular language versions of the article "Atiyah–Singer index theorem" in all the time

#	Language	Popularity award	Relative popularity
1	English (en) Atiyah–Singer index theorem		631 956
2	Japanese (ja) アティヤ＝シンガーの指数定理		94 852
3	German (de) Atiyah-Singer-Indexsatz		54 017
4	French (fr) Théorème de l'indice d'Atiyah-Singer		42 841
5	Chinese (zh) 阿蒂亞-辛格指標定理		33 462
6	Russian (ru) Теорема Атьи — Зингера об индексе		15 827
7	Korean (ko) 아티야-싱어 지표 정리		9 753
8	Italian (it) Teorema di Atiyah-Singer		7 760
9	Portuguese (pt) Teorema do índice de Atiyah-Singer		5 237
10	Arabic (ar) نظرية أس عطية-سينجر		3 444

More...

The following table shows the language versions of the article with the highest popularity in the last month.

The most popular language versions of the article "Atiyah–Singer index theorem" in October 2023

#	Language	Popularity award	Relative popularity
1	English (en) Atiyah–Singer index theorem		23 396
2	Japanese (ja) アティヤ＝シンガーの指数定理		479
3	Russian (ru) Теорема Атьи — Зингера об индексе		241
4	Chinese (zh) 阿蒂亞-辛格指標定理		198
5	French (fr) Théorème de l'indice d'Atiyah-Singer		162
6	German (de) Atiyah-Singer-Indexsatz		155
7	Greek (el) Θεώρημα δείκτη Ατίγια-Σίνγκερ		127
8	Spanish (es) Teorema del índice de Atiyah-Singer		42
9	Korean (ko) 아티야-싱어 지표 정리		42
10	Italian (it) Teorema di Atiyah-Singer		33

More...

The following table shows the language versions of the article with the highest Authors’ Interest.

Language versions of the article "Atiyah–Singer index theorem" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.

#	Language	AI award	Relative AI
1	English (en) Atiyah–Singer index theorem		107
2	German (de) Atiyah-Singer-Indexsatz		51
3	Japanese (ja) アティヤ＝シンガーの指数定理		24
4	French (fr) Théorème de l'indice d'Atiyah-Singer		16
5	Chinese (zh) 阿蒂亞-辛格指標定理		11
6	Greek (el) Θεώρημα δείκτη Ατίγια-Σίνγκερ		10
7	Portuguese (pt) Teorema do índice de Atiyah-Singer		9
8	Russian (ru) Теорема Атьи — Зингера об индексе		9
9	Spanish (es) Teorema del índice de Atiyah-Singer		6
10	Italian (it) Teorema di Atiyah-Singer		6

More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

Language versions of the article "Atiyah–Singer index theorem" with the highest AI in October 2023

#	Language	AI award	Relative AI
1	Greek (el) Θεώρημα δείκτη Ατίγια-Σίνγκερ		1
2	Spanish (es) Teorema del índice de Atiyah-Singer		1
3	French (fr) Théorème de l'indice d'Atiyah-Singer		1
4	Arabic (ar) نظرية أس عطية-سينجر		0
5	Catalan (ca) Teorema de l'índex d'Atiyah-Singer		0
6	German (de) Atiyah-Singer-Indexsatz		0
7	English (en) Atiyah–Singer index theorem		0
8	Basque (eu) Atiyah-Singer indizearen teorema		0
9	Persian (fa) قضیه اندیس عطیه-سینگر		0
10	Galician (gl) Teorema do índice de Atiyah-Singer		0

More...

The following table shows the language versions of the article with the highest number of citations.

Language versions of the article "Atiyah–Singer index theorem" with the highest Citation Index (CI)

#	Language	CI award	Relative CI
1	English (en) Atiyah–Singer index theorem		721
2	German (de) Atiyah-Singer-Indexsatz		60
3	Japanese (ja) アティヤ＝シンガーの指数定理		43
4	French (fr) Théorème de l'indice d'Atiyah-Singer		36
5	Korean (ko) 아티야-싱어 지표 정리		23
6	Chinese (zh) 阿蒂亞-辛格指標定理		22
7	Russian (ru) Теорема Атьи — Зингера об индексе		14
8	Ukrainian (uk) Теорема Атії — Зінгера про індекс		9
9	Portuguese (pt) Teorema do índice de Atiyah-Singer		7
10	Spanish (es) Teorema del índice de Atiyah-Singer		6

More...

#	Language	Value
ar	Arabic نظرية أس عطية-سينجر
ca	Catalan Teorema de l'índex d'Atiyah-Singer
de	German Atiyah-Singer-Indexsatz
el	Greek Θεώρημα δείκτη Ατίγια-Σίνγκερ
en	English Atiyah–Singer index theorem
es	Spanish Teorema del índice de Atiyah-Singer
eu	Basque Atiyah-Singer indizearen teorema
fa	Persian قضیه اندیس عطیه-سینگر
fr	French Théorème de l'indice d'Atiyah-Singer
gl	Galician Teorema do índice de Atiyah-Singer
it	Italian Teorema di Atiyah-Singer
ja	Japanese アティヤ＝シンガーの指数定理
ko	Korean 아티야-싱어 지표 정리
nl	Dutch Indexstelling van Atiyah-Singer
pt	Portuguese Teorema do índice de Atiyah-Singer
ru	Russian Теорема Атьи — Зингера об индексе
sr	Serbian Ati–Zingerova indeksna teorema
tr	Turkish Atiyah–Singer indeks teoremi
uk	Ukrainian Теорема Атії — Зінгера про індекс
zh	Chinese 阿蒂亞-辛格指標定理

Best Rank

English: #51305 10.2023

Global: #93281 10.2023

Best Rank

English: #6250 09.2003

Global: #14445 09.2003

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The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from November, 2023. When calculating current popularity and AI of articles data from October 2023 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2023... More information