Bøger i New Mathematical Monographs serien

Property (T) is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property (T) plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property (T): the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property (T).

This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras, and there is also a full account of localization. Each chapter has a number of exercises plus open problems and historical notes.

The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which underlie the work of Cohen, Moore, and the author. Suitable for a course in unstable homotopy theory, it is also a valuable reference for experts and graduate students alike.

This self-contained 2010 account of the state of the art in classical complex multiplication provides an exhaustive treatment of the theory of elliptic functions, modular functions and quadratic number fields. The reader will find all the necessary background and tools they will need in this book.

Hilbert's Tenth Problem - to find an algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions - was shown to be unsolvable in the late sixties. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields.

Students learning the subject from scratch will value this comprehensive text, which presents three major types of dynamics, from the basics to some of the latest results: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. It will also be a valuable reference for experienced researchers.

The first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. The author presents its mathematical foundations, demonstrating its relation to classical algebraic topology, and explores its varied applications.

This is a unified exposition of the theory of symmetric designs with emphasis on recent developments. The authors cover the combinatorial aspects of the theory giving particular attention to the construction of symmetric designs and related objects. For all researchers in combinatorial designs, coding theory, and finite geometries.

The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. Following an extensive discussion of many current approaches, Carlos Simpson explains the first concrete and workable theory of n-categories in detail.

In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. The book covers applications in pure and applied mathematics and in mechanics, and it will interest researchers and graduate students in these areas.

An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

This rich mathematical text will help both graduate students and researchers master modern topology and domain theory, the key mathematics behind the semantics of computer languages. It deals with elementary and advanced concepts of topology and the theory is illuminated by many examples, figures and more than 450 exercises.

This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.

This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. This second edition has been revised and updated, with Chapter 9 being completely rewritten via the useful new notion of 'minimal type' for pseudo-reductive groups.

Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincare inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincare inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincare inequalities under Gromov-Hausdorff convergence, and the Keith-Zhong self-improvement theorem for Poincare inequalities.