Overview

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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Author:   Paolo Piazza ,  Thomas Schick ,  Vito Felice Zenobi
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470473174

ISBN 10:   1470473178
Pages:   145
Publication Date:   30 June 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Forthcoming
Availability:   Not yet available  
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Table of Contents

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

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Author Information

Paolo Piazza, Sapienza Universita Di Roma, Italy, Thomas Schick, Georg-August Universitat Gottingen, Germany. Vito Felice Zenobi, Instituto Nazionale di Alta Matematica, Roma, Italy.

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