# Noncommutative Geometry and Global Analysis

Share this page *Edited by *
*Alain Connes; Alexander Gorokhovsky; Matthias Lesch; Markus Pflaum; Bahram Rangipour*

This volume represents the proceedings of the conference on
Noncommutative Geometric Methods in Global Analysis, held in honor of
Henri Moscovici, from June 29–July 4, 2009, in Bonn, Germany.

Henri Moscovici has made a number of major contributions to
noncommutative geometry, global analysis, and representation theory.
This volume, which includes articles by some of the leading experts in
these fields, provides a panoramic view of the interactions of
noncommutative geometry with a variety of areas of mathematics. It
focuses on geometry, analysis and topology of manifolds and singular
spaces, index theory, group representation theory, connections of
noncommutative geometry with number theory and arithmetic geometry, Hopf
algebras and their cyclic cohomology.

#### Readership

Graduate students and research mathematicians interested in noncommutative geometry and its relations to other areas of mathematics.

# Table of Contents

## Noncommutative Geometry and Global Analysis

- Contents v6 free
- Introduction vii8 free
- Conference Talks xi12 free
- List of Participants xix20 free
- Dirac cohomology and unipotent representations of complex groups 122 free
- Algebraic index theorem for symplectic deformations of gerbes 2344
- Index theory for basic Dirac operators on Riemannian foliations 3960
- 1. Introduction 4061
- 2. Riemannian foliations and basic Dirac operators 4162
- 3. Fredholm properties and equivariant theory 4970
- 4. Desingularization of the foliation 6081
- 5. The equivariant index theorem 6485
- 6. The basic index theorem 6687
- 7. The representation-valued basic index theorem 6889
- 8. The basic index theorem for foliations given by suspension 6889
- 9. An example of transverse signature 7091
- 10. The Basic Euler characteristic 7192
- References 79100

- The Witt construction in characteristic one and quantization 83104
- Lie prealgebras 115136
- 1. Introduction 116137
- 2. Lie algebras, PBW property, etc. 116137
- 3. Associative algebras 118139
- 4. Quadratic algebras 119140
- 5. Examples I 121142
- 6. Nonhomogeneous quadratic algebras 123144
- 7. Duality 125146
- 8. Examples II 126147
- 9. Lie prealgebras 128149
- 10. Complexes and homologies 131152
- 11. Further prospects (tentative conclusion) 134155
- References 134155

- On the analogy between complex semisimple groups and their Cartan motion groups 137158
- A survey on Hopf-cyclic cohomology and Connes-Moscovici characteristic map 171192
- A super version of Connes-Moscovici Hopf algebra 181202
- Analytic torsion of Z2-graded elliptic complexes 199220
- The K-groups and the index theory of certain comparison C*-algebras 213234
- Relative pairings and the Atiyah-Patodi-Singer index formula for the Godbillon-Vey cocycle 225246
- Two exact sequences for lattice cohomology 249270
- Cup products in Hopf cyclic cohomology with coefficients in contramodules 271292
- Algebras of p-symbols, noncommutative p-residue, and the Brauer group 283304
- Large scale geometry and its applications 305326