阿蒂亞-辛格指標定理

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 “阿蒂亞-辛格指標定理” in Chinese Wikipedia has 30.1 points for quality (as of July 1, 2025). The article contains 0 references and 21 sections.

This article has the best quality in English Wikipedia. Also, this article is the most popular in that (Chinese) language version.

Since the creation of article “阿蒂亞-辛格指標定理”, its content was written by 13 registered users of Chinese Wikipedia and edited by 305 registered Wikipedia users in all languages.

The article is cited 24 times in Chinese Wikipedia and cited 1068 times in all languages.

The highest Authors Interest rank from 2001:

• Local (Chinese): #17025 in April 2008
• Global: #14435 in September 2003

The highest popularity rank from 2008:

• Local (Chinese): #53243 in September 2018
• Global: #90140 in November 2023

There are 21 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 July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

#	Language	Quality grade	Quality score
1	English (en) Atiyah–Singer index theorem		50.2207
2	Basque (eu) Atiyah-Singer indizearen teorema		40.9286
3	Catalan (ca) Teorema de l'índex d'Atiyah-Singer		38.134
4	German (de) Atiyah-Singer-Indexsatz		35.5525
5	Spanish (es) Teorema del índice de Atiyah-Singer		35.5129
6	Chinese (zh) 阿蒂亞-辛格指標定理		30.1285
7	Greek (el) Θεώρημα δείκτη Ατίγια-Σίνγκερ		29.332
8	Korean (ko) 아티야-싱어 지표 정리		28.0013
9	Serbian (sr) Ati–Zingerova indeksna teorema		25.9978
10	Persian (fa) قضیه اندیس عطیه-سینگر		25.1537

More...

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

The most popular language versions of the article "阿蒂亞-辛格指標定理" in all the time

#	Language	Popularity award	Relative popularity
1	English (en) Atiyah–Singer index theorem		749 829
2	Japanese (ja) アティヤ＝シンガーの指数定理		104 645
3	German (de) Atiyah-Singer-Indexsatz		58 017
4	French (fr) Théorème de l'indice d'Atiyah-Singer		47 377
5	Chinese (zh) 阿蒂亞-辛格指標定理		38 812
6	Russian (ru) Теорема Атьи — Зингера об индексе		18 908
7	Korean (ko) 아티야-싱어 지표 정리		10 929
8	Italian (it) Teorema di Atiyah-Singer		8 806
9	Portuguese (pt) Teorema do índice de Atiyah-Singer		5 888
10	Arabic (ar) نظرية أس عطية-سينجر		4 142

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 "阿蒂亞-辛格指標定理" in June 2025

#	Language	Popularity award	Relative popularity
1	English (en) Atiyah–Singer index theorem		3 614
2	Japanese (ja) アティヤ＝シンガーの指数定理		550
3	Chinese (zh) 阿蒂亞-辛格指標定理		238
4	French (fr) Théorème de l'indice d'Atiyah-Singer		217
5	German (de) Atiyah-Singer-Indexsatz		131
6	Russian (ru) Теорема Атьи — Зингера об индексе		115
7	Greek (el) Θεώρημα δείκτη Ατίγια-Σίνγκερ		62
8	Spanish (es) Teorema del índice de Atiyah-Singer		46
9	Korean (ko) 아티야-싱어 지표 정리		40
10	Portuguese (pt) Teorema do índice de Atiyah-Singer		35

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

Language versions of the article "阿蒂亞-辛格指標定理" 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		108
2	German (de) Atiyah-Singer-Indexsatz		52
3	Japanese (ja) アティヤ＝シンガーの指数定理		26
4	French (fr) Théorème de l'indice d'Atiyah-Singer		22
5	Chinese (zh) 阿蒂亞-辛格指標定理		13
6	Greek (el) Θεώρημα δείκτη Ατίγια-Σίνγκερ		12
7	Italian (it) Teorema di Atiyah-Singer		11
8	Portuguese (pt) Teorema do índice de Atiyah-Singer		9
9	Russian (ru) Теорема Атьи — Зингера об индексе		9
10	Spanish (es) Teorema del índice de Atiyah-Singer		7

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

Language versions of the article "阿蒂亞-辛格指標定理" with the highest AI in June 2025

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

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

Language versions of the article "阿蒂亞-辛格指標定理" with the highest Citation Index (CI)

#	Language	CI award	Relative CI
1	English (en) Atiyah–Singer index theorem		731
2	German (de) Atiyah-Singer-Indexsatz		62
3	Japanese (ja) アティヤ＝シンガーの指数定理		45
4	Ukrainian (uk) Теорема Атії — Зінгера про індекс		41
5	French (fr) Théorème de l'indice d'Atiyah-Singer		36
6	Korean (ko) 아티야-싱어 지표 정리		27
7	Greek (el) Θεώρημα δείκτη Ατίγια-Σίνγκερ		26
8	Chinese (zh) 阿蒂亞-辛格指標定理		24
9	Russian (ru) Теорема Атьи — Зингера об индексе		16
10	Spanish (es) Teorema del índice de Atiyah-Singer		8

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
fi	Finnish Atiyahin–Singerin indeksilause
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

Chinese: #53243 09.2018

Global: #90140 11.2023

Best Rank

Chinese: #17025 04.2008

Global: #14435 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 July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information