Jean-Pierre Otal, ENS-Lyon, France
The Hyperbolization Theorem for Fibered 3-manifolds
Not yet published.
Expected publication date is October 8, 2001
Description
A fundamental element of the study of 3-manifolds is Thurston's remarkable geometrization conjecture, which states that the interior of every compact 3-manifold has a canonical decomposition into pieces that have geometric structures. In most cases, these structures are complete metrics of constant negative curvature, that is to say, they are hyperbolic manifolds. The conjecture has been proved in some important cases, such as Haken manifolds and certain types of fibered manifolds. The influence of Thurston's hyperbolization theorem on the geometry and topology of 3-manifolds has been tremendous. This book presents a complete proof of the hyperbolization theorem for 3-manifolds that fiber over the circle, following the plan of Thurston's original (unpublished) proof, though the double limit theorem is dealt with in a different way.
The book is suitable for graduate students with a background in modern techniques of low-dimensional topology and will also be of interest to researchers in geometry and topology.
This is the English translation of a volume originally published in 1996 by the Societe Mathematique de France.
Contents
Teichmuller spaces and Kleinian groups
Real trees and degenerations of hyperbolic structures
Geodesic laminations and real trees
Geodesic laminations and the Gromov topology
The double limit theorem
The hyperbolization theorem for fibered manifolds
Sullivan's theorem
Actions of surface groups on real trees
Two examples of hyperbolic manifolds that fiber over the circle
Geodesic laminations
Bibliography
Index
Details:
Series: SMF/AMS Texts and Monographs, Volume: 7
Publication Year: 2001
ISBN: 0-8218-2153-9
Paging: approximately 133 pp.
Binding: Softcover
Te Sun Han and Kingo Kobayashi, The University of Electro-Communications, Tokyo, Japan
Mathematics of Information and Coding
Expected publication date is December 2, 2001
Description
This book is intended to provide engineering and/or statistics students, communications engineers, and mathematicians with the firm theoretic basis of source coding (or data compression) in information theory. Although information theory consists of two main areas, source coding and channel coding, the authors choose here to focus only on source coding. The reason is that, in a sense, it is more basic than channel coding, and also because of recent achievements in source coding and compression. An important feature of the book is that whenever possible, the author describes universal coding methods, i.e., the methods that can be used without prior knowledge of the statistical properties of the data. The authors approach the subject of source coding from the very basics to the top frontiers in an intuitively transparent, but mathematically sound manner.
The book serves as a theoretical reference for communication professionals and statisticians specializing in information theory. It will also serve as an excellent introductory text for advanced-level and graduate students taking elementary or advanced courses in telecommunications, electrical engineering, statistics, mathematics, and computer science.
Contents
What is information theory?
Basics of information theory
Source and coding
Arithmetic code
Universal coding of integers
Universal coding of texts
Universal coding of compound sources
Data analysis and MDL principle
Bibliography
Index
Details:
Series: Translations of Mathematical Monographs, Publication Year: 2001
ISBN: 0-8218-0534-7
Paging: approximately 296 pp.
Binding: Hardcover
Dwyer , W.G., University of Notre Dame, Notre Dame, Indiana, USA,
Henn, H.-W., Universite Louis Pasteur, Strasbourg
Homotopy Theoretic Methods in Group Cohomology
2001. Approx. 108 pages. Softcover
ISBN 3-7643-6605-2
English
Due in October 2001
CRM Barcelona
Advanced Courses in Mathematics
This book looks at group cohomology with tools that come from homotopy theory. These tools give both decomposition theorems (which rely on homotopy colimits to obtain a description of the cohomology of a group in terms of the cohomology of suitable subgroups) and global structure theorems (which exploit the action of the ring of topological cohomology operations). The approach is expository and thus suitable for graduate students and others who would like an introduction to the subject that organizes and adds to the relevant literature and leads to the frontier of current research. The book should also be interesting to anyone who wishes to learn some of the machinery of homotopy theory (simplicial sets, homotopy colimits, Lannes' T-functor, the theory of unstable modules over the Steenrod algebra) by seeing how it is used in a practical setting.
Sohr, H., University of Paderborn, Germany
The Navier-Stokes Equations
An Elementary Functional Analytic Approach
2001. 384 pages. Hardcover
ISBN 3-7643-6545-5
English
Due in September 2001
Birkhauser Advanced Texts
The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes.
Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one.
Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers' convenience, some fundamental properties of, for example, Sobolev spaces, distributions and operators are collected in the first two chapters.
Huckleberry, A., Ruhr-Universitat Bochum, Germany,
Wurzbacher , T., Universite Louis Pasteur, Strasbourg, France, (Eds.)
Infinite Dimensional Kahler Manifolds
2001. 392 pages. Softcover
ISBN 3-7643-6602-8
English
DMV Seminar, Vol. 31
Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest.
On the one hand this is a collection of closely related articles on infinite dimensional Kahler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas.
The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.