Equivariant E-theory for C*-algebras / Erik Guentner, Nigel Higson, Jody Trout.
Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups E G(A, B) which generalize the E-theory groups of Connes and Higson. We develo...
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| Language: | English |
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Providence, R.I. :
American Mathematical Society,
©2000.
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| Series: | Memoirs of the American Mathematical Society ;
no. 703. |
| Subjects: |
MARC
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| 100 | 1 | |a Guentner, Erik, |d 1965- | |
| 245 | 1 | 0 | |a Equivariant E-theory for C*-algebras / |c Erik Guentner, Nigel Higson, Jody Trout. |
| 260 | |a Providence, R.I. : |b American Mathematical Society, |c ©2000. | ||
| 300 | |a 1 online resource (viii, 86 pages) | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
| 338 | |a online resource |b cr |2 rdacarrier. | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 1947-6221 ; |v v. 703. | |
| 504 | |a Includes bibliographical references (pages 85-86) | ||
| 505 | 0 | 0 | |t Introduction |t 1. Asymptotic morphisms |t 2. The homotopy category of asymptotic morphisms |t 3. Functors on the homotopy category |t 4. Tensor products and descent |t 5. $C$*-algebra extensions |t 6. E-theory |t 7. Cohomological properties |t 8. Proper algebras |t 9. Stabilization |t 10. Assembly |t 11. The Green-Julg theorem |t 12. Induction and compression |t 13. A generalized Green-Julg theorem |t 14. Application to the Baum-Connes conjecture |t 15. Concluding remark on assembly for proper algebras. |
| 520 | 8 | |a Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups E G(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in recent work of Higson and Kasparov on the Baum-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space. | |
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a KK-theory. | |
| 650 | 0 | |a C*-algebras. | |
| 650 | 7 | |a C*-algebras. |2 fast |0 (OCoLC)fst00843285. | |
| 650 | 7 | |a KK-theory. |2 fast |0 (OCoLC)fst00985553. | |
| 700 | 1 | |a Higson, Nigel, |d 1963- | |
| 700 | 1 | |a Trout, Jody. | |
| 776 | 0 | 8 | |i Print version: |a Guentner, Erik, 1965- |t Equivariant E-theory for C*-algebras / |x 0065-9266 |z 9780821821169. |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 703. | |
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