Books in the Oxford Mathematical Monographs series
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This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
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This book gives a complete and self-contained account of what is known about this subject and is written from a geometrical and analytical point of view, with quantum field theory very much in mind.
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This text deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincare inequalities.
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This book is a systematic presentation of the solution of one of the fundamental problems of the theory of random dynamical systems - the problem of topological classification and structural stability of linear hyperbolic random dynamical systems.
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Covering projective geometries over finite fields, this book is intended for researchers in mathematics, particularly in the areas of finite geometry, combinatorics and coding theory. It may also interest postgraduate students and final year students in these areas.
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Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behaviour of a wide range of physical systems. This is a comprehensive introduction to the subject. It also includes a discussion of Taubes and Donaldson's contributions ...to the subject.
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By D'Eath, P. D.
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This work starts with a survey of the standard theory of black holes, and then studies, analytically, the interaction of a black hole with another strongly self-gravitating system (such as the extra universe on and through black holes).
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Provides an accessible account to the modern study of the geometry of four-manifolds. This title is suitable for postgraduates and research workers. The central theme is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Y...ang-Mills theory and anti-self dual connections over four-manifolds.
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The geometric approach to quantization was introduced by Kostant and Souriau more than 20 years ago and has given insights into the relationship between classical and quantum systems. This revised edition explores geometric quantization with expanded material on field theory.
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Aims to provide a detailed account in this field. The emphasis is on infinite groups, although some relevant theorems on finite products of groups are also proved. The chapter on splitting and conjugacy theorems is very new and should be of independent interest.
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