**Fields Institute Communications**

Volume: 61;
2011;
163 pp;
Hardcover

MSC: Primary 58;
Secondary 19; 16; 18

Print ISBN: 978-0-8218-4849-4

Product Code: FIC/61

List Price: $94.00

AMS Member Price: $75.20

MAA member Price: $84.60

**Electronic ISBN: 978-1-4704-1782-6
Product Code: FIC/61.E**

List Price: $94.00

AMS Member Price: $75.20

MAA member Price: $84.60

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# Perspectives on Noncommutative Geometry

Share this page *Edited by *
*Masoud Khalkhali; Guoliang Yu*

A co-publication of the AMS and Fields Institute

This volume represents the proceedings of the Noncommutative Geometry
Workshop that was held as part of the thematic program
on operator algebras at the Fields Institute in May 2008.

Pioneered by Alain Connes starting in the late 1970s,
noncommutative geometry was originally inspired by global analysis,
topology, operator algebras, and quantum physics. Its main
applications were to settle some long-standing conjectures, such as
the Novikov conjecture and the Baum-Connes conjecture.

Next came the impact of spectral geometry and the way the spectrum
of a geometric operator, like the Laplacian, holds information about
the geometry and topology of a manifold, as in the celebrated Weyl
law. This has now been vastly generalized through Connes' notion of
spectral triples.

Finally, recent years have witnessed the impact of number theory,
algebraic geometry and the theory of motives, and quantum field theory
on noncommutative geometry. Almost all of these aspects are touched
upon with new results in the papers of this volume.

This book is intended for graduate students and researchers in both
mathematics and theoretical physics who are interested in
noncommutative geometry and its applications.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Readership

Graduate students and research mathematicians interested in noncommutative geometry.

# Table of Contents

## Perspectives on Noncommutative Geometry

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Local index theorem for projective families 110
- Type III KMS states on a class of 𝐶*-algebras containing 𝑂_{𝑛} and 𝒬_{𝒩} and their modular index 2938
- Duality, correspondences and the Lefschetz map in equivariant KK-theory: A survey 4150
- Twisted spectral triples and Connes’ character formula 7988
- Spectral morphisms, K-theory, and stable ranks 103112
- A survey of braided Hopf cyclic cohomology 117126
- A survey of Rankin-Cohen deformations 133142
- Pseudo-differential operators and regularity of spectral triples 153162
- Back Cover Back Cover1176