Mapping Analytic Surgery to Homology, Higher Rho Numbers and Metrics ofPositive Scalar Curvature

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