The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
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ISBN-13
978-1-4704-7317-4 (9781470473174)
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Schweitzer Klassifikation
Paolo Piazza, Sapienza Universita Di Roma, Italy, Thomas Schick, Georg-August Universitat Gottingen, Germany.
Vito Felice Zenobi, Instituto Nazionale di Alta Matematica, Roma, Italy.
Chapters
1. Introduction
2. The relation between the structure algebra $D^*(\widetilde {M})^\Gamma $ and $\mathrm {\Psi }^0_\Gamma (\widetilde {M})$
3. Rho classes
4. Non-commutative de Rham homology and Chern characters
5. Pseudodifferential operators and smooth subalgebras
6. Mapping analytic surgery to homology
7. Higher rho numbers associated to elements in $HC^* (\mathbb {C}\Gamma ,\langle x \rangle )$
8. Higher rho numbers from relative cohomology $H^*(M\to B\Gamma )$
9. Delocalized higher Atiyah-Patodi-Singer indices
10. The space of metrics of positive scalar curvature and higher rho-invariants
11. Naturality for the action by the diffeomorphism group
12. The role of real K-theory
13. Geometric applications of delocalized cyclic cohomology
14. Geometric applications of relative cohomology
15. Geometric applications: A topological approach
16. Concluding remarks
