Twisted K-theory
Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C*-algebras. Up to equivalence, the twisting corresponds to an element of H³(X; Z). We give a systematic account of the definition and basic properties of the...
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| Опубліковано в: : | Український математичний вісник |
|---|---|
| Дата: | 2004 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2004
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/124621 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Twisted K-theory / M. Atiyah, G. Segal // Український математичний вісник. — 2004. — Т. 1, № 3. — С. 287-330. — Бібліогр.: 29 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862554620186853376 |
|---|---|
| author | Atiyah, M. Segal, G. |
| author_facet | Atiyah, M. Segal, G. |
| citation_txt | Twisted K-theory / M. Atiyah, G. Segal // Український математичний вісник. — 2004. — Т. 1, № 3. — С. 287-330. — Бібліогр.: 29 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C*-algebras. Up to equivalence, the twisting corresponds to an element of H³(X; Z). We give a systematic account of the definition and basic properties of the twisted theory, emphasizing some points where it behaves differently from ordinary K-theory. (We omit, however, its relations to classical cohomology, which we shall treat in a sequel.) We develop an equivariant version of the theory for the action of a compact Lie group, proving that then the twistings are classified by the equivariant cohomology group H³G (X; Z). We also consider some basic examples of twisted K-theory classes, related to those appearing in the recent work of Freed-Hopkins-Teleman.
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| first_indexed | 2025-11-25T21:46:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-124621 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-11-25T21:46:07Z |
| publishDate | 2004 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Atiyah, M. Segal, G. 2017-09-30T11:09:53Z 2017-09-30T11:09:53Z 2004 Twisted K-theory / M. Atiyah, G. Segal // Український математичний вісник. — 2004. — Т. 1, № 3. — С. 287-330. — Бібліогр.: 29 назв. — англ. 1810-3200 2000 MSC. 55-xx, 55N15, 55N91, 19Kxx. https://nasplib.isofts.kiev.ua/handle/123456789/124621 Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C*-algebras. Up to equivalence, the twisting corresponds to an element of H³(X; Z). We give a systematic account of the definition and basic properties of the twisted theory, emphasizing some points where it behaves differently from ordinary K-theory. (We omit, however, its relations to classical cohomology, which we shall treat in a sequel.) We develop an equivariant version of the theory for the action of a compact Lie group, proving that then the twistings are classified by the equivariant cohomology group H³G (X; Z). We also consider some basic examples of twisted K-theory classes, related to those appearing in the recent work of Freed-Hopkins-Teleman. en Інститут прикладної математики і механіки НАН України Український математичний вісник Twisted K-theory Article published earlier |
| spellingShingle | Twisted K-theory Atiyah, M. Segal, G. |
| title | Twisted K-theory |
| title_full | Twisted K-theory |
| title_fullStr | Twisted K-theory |
| title_full_unstemmed | Twisted K-theory |
| title_short | Twisted K-theory |
| title_sort | twisted k-theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124621 |
| work_keys_str_mv | AT atiyahm twistedktheory AT segalg twistedktheory |