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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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2004
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| Series: | Український математичний вісник |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/124621 |
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| 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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