Mapping Analytic Surgery to Homology, Higher Rho Numbers and Metrics of Positive Scalar Curvature
Published on 31. August 2025
Book
Paperback/Softback
145 pages
978-1-4704-7317-4 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Illustrations
254
ISBN-13
978-1-4704-7317-4 (9781470473174)
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Schweitzer Classification
Persons
Paolo Piazza, Sapienza Universita Di Roma, Italy, Thomas Schick, Georg-August Universitat Gottingen, Germany.
Vito Felice Zenobi, Instituto Nazionale di Alta Matematica, Roma, Italy.
Vito Felice Zenobi, Instituto Nazionale di Alta Matematica, Roma, Italy.
Content
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
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