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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| Published in: | Український математичний вісник |
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| Date: | 2004 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2004
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/124621 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Twisted K-theory / M. Atiyah, G. Segal // Український математичний вісник. — 2004. — Т. 1, № 3. — С. 287-330. — Бібліогр.: 29 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1810-3200 |