Cuntz, J., University of Munster, Germany
Echterhoff, S., University of Munster, Germany
(Eds.)
C*-Algebras
2000. VIII, 272 pp.
3-540-67562-0
This book represents the refereed proceedings of the SFB-Workshop on C*-Algebras which was held at
MEster in March 1999. It contains articles by some of the best researchers on the subject of C*-algebras
about recent developments in the field of C*-algebra theory and its connections to harmonic analysis and
noncommutative geometry. Among the contributions there are several excellent surveys and overviews and
some original articles covering areas like the classification of C*-algebras, K-theory, exact C*-algebras and
exact groups, Cuntz-Krieger-Pimsner algebras, group C*-algebras, the Baum-Connes conjecture and others.
Keywords: C * -algebras, K-theory, Cuntz-Krieger-Pimsner algebras, Baum-Connes conjecture
Contents: From the contents: B. Bekka/N. Louvet: Some Properties of C*-Algebras Associated to Discrete
Linear Groups.- B. Blackadar/E. Kirchberg: Generalized Inductive Limits and Quasidiagonality.- M. Dadarlat:
Approximate Unitary Equivalence and the Topology of Ext(A,B) - K.J. Dykema: Free Products of Exact
Groups.- U. Haagerup/S. Thorbjornsen: Random Matrices and Non-Exact C*-Algebras.- T. Natsume:
C*-Algebraic Deformation Quantization of Closed Riemann Surfaces.- R. Nest/F. Radulescu: Index of
Gamma-Equivariant Toeplitz Operators.- I. Raeburn/A. Sims/D.P. Williams: Twisted Actions and
Obstructions in Group Cohomology.- G. Robertson: Boundary Actions for Affine Buildings and Higher
Rank Cuntz-Krieger Algebras.- J. Schweizer: Crossed Products by C*-Correspondences and Cuntz-Pimsner
Algebras.- J.-L. Tu: The Baum-Connes Conjecture for Groupoids.- S. Wassermann: C*-Exact Groups.
The complete table of contents can be found on the Internet: http://www.springer.de/cgi-bin/search
book.pl?isbn=3-540-67562-0
Smith, G., University of Bath, UK
Tabachnikova, O., University of Bath, UK
Topics in Group Theory
2000. XVI, 255 pp. 16 figs.
1-85233-235-2
The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed
to support a reader engaged in a first serious group theory course, or a mathematically mature reader
approaching the subject for the first time, this book reviews the essentials. It recaps the basic definitions
and results, up to and including Lagrange's Theorem, and then continues to explore topics such as the
isomorphism theorems and group actions. Later chapters include material on chain conditions and
finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of
"entertainments" takes the basic theory and plays with it to obtain an assortment of results that will show a
little of what can be done with the theoretical machinery.
Adopting the slightly irreverent tone of Geoff Smith's previous book "Introductory Mathematics: Algebra
and Analysis" this book is a key reference that will both stimulate and entertain its readers.
Contents: The Elements.- Structure.- Action.- Fun and Games.- Law.- Presentations.- Appendix A: Fields.-
Appendix B: Relations and Orderings.- Solutions.- Index.
Series: Springer Undergraduate Mathematics Series.
Diejen, J.F.van, University of Chile, Santiago, Chile
Vinet, L., McGill University, Montreal, Que., Canada
(Eds.)
Calogero-Moser-Sutherland Models
2000. XXV, 561 pp. 27 figs.
0-387-98968-4
In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional
systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until
then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J.
Moser subsequently showed that the classical counterparts to these models is also amenable to an exact
analytical approach. The last decade has witnessed a true explosion of activities involving
Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical
physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical
mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation
theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical
systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of
the many branches into which research on CMS systems has diversified in recent years. The contributions
are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic
of investigation itself or as a tool for further applications.
Series: CRM Series in Mathematical Physics.
Lee, J.M., University of Washington, Seattle, WA, USA
Introduction to Topological Manifolds
2000. Approx. 400 pp. 194 figs.
0-387-95026-5
This book is an introduction to manifolds at the beginning graduate level. It contains the essential
topological ideas that are needed for the further study of manifolds, particularly in the context of differential
geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas
rigorously but economically, with minimal prerequisites and plenty of geometric intuition. A course on
manifolds differs from most other introductory mathematics graduate courses in that the subject matter is
often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates,
manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate
mathematics education without ever hearing the word "manifold." Yet manifolds are part of the basic
vocabulary of modern mathematics, and students need to know them as intimately as they know the
integers, the real numbers, Euclidean spaces, groups, rings, and fields. In his beautifully conceived
introduction, the author motivates the technical developments to follow by explaining some of the roles
manifolds play in diverse branches of mathematics and physics. Then he goes on to introduce the basics of
general topology and continues with the fundamental group, covering spaces, and elementary homology
theory. Manifolds are introduced early and used as the main examples throughout. John M. Lee is currently
Professor of Mathematics at the University of Washington.
Contents: Introduction.- General Topology.- New Spaces From Old.- Compactness and Connectedness.-
Surfaces.- Homotopy and the Fundamental Group.- The Circle.- Some Group Theory.- Fundamental Groups
of Surfaces.- Covering Spaces.- Classification of Covering Spaces.
Series: Graduate Texts in Mathematics.VOL. 202