Topology

This book describes work, largely that of the author, on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel-Whitney classes. Using techniques from homological group...

This work provides a lucid and rigorous account of the foundations of algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but...

This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete,...

The theory of surfaces has reached a certain stage of completeness and major efforts concentrate on solving concrete questions rather than developing further the formal theory. Many of these questions are touched upon in this classic volume: such as the...

Twistor theory has become a diverse subject as it has spread from its origins in theoretical physics to applications in pure mathematics. This 1990 collection of review articles covers the considerable progress made in a wide range of applications such...

This book, which grew out of Steven Bleiler's lecture notes from a course given by Andrew Casson at the University of Texas, is designed to serve as an introduction to the applications of hyperbolic geometry to low dimensional topology. In particular it...

This volume will give a systematic exposition of known results for free actions by finite groups on S. The text begins with preliminary material on Seifert manifolds and group classification. This is followed by sections dealing with related topics...

Mathematicians have developed the language of topology; but the conventional development leaves until last the discussion and ideas about shapes, so those who have not mastered the initial ideas of analysis and general topology are barred from...

Finsler geometry generalises Riemannian geometry in the same sense that Banach spaces generalise Hilbert spaces. This book presents an expository account of seven important topics in Riemann-Finsler geometry, ones which have undergone significant...

This volume consists of the proceedings of a conference held at the University College of North Wales (Bangor) in July of 1979. It assembles research papers which reflect diverse currents in low-dimensional topology. The topology of 3-manifolds,...

This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms...

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Eleven of the fourteen invited speakers at a symposium held by the Oxford Mathematical Institute in June 1972 have revised their contributions and submitted them for publication in this volume. The present papers do not necessarily closely correspond...

Multiplicity diagrams can be viewed as schemes for describing the phenomenon of 'symmetry breaking' in quantum physics. The subject of this book is the multiplicity diagrams associated with the classical groups U(n), O(n), etc. It presents such topics as...

This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems and special attention is given to the results needed in the...

This book documents the focus on a branch of Riemannian geometry called Comparison Geometry. The simple idea of comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has seen a tremendous evolution of...

The central theme of the book is the development of the idea of congruence, that relation between geometric figures which is basic to ordinary Euclidean geometry. The text is divided into four books corresponding to stages in the development of a...

Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development of algebraic topology. This monograph provides an account of the subject which bridges the gap between the fundamental...

This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written...

This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing 17 survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository:...

These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the...

Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for...

Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is...

The new student in differential and low-dimensional topology is faced with a bewildering array of tools and loosely connected theories. This short book presents the essential parts of each, enabling the reader to become 'literate' in the field and begin...

This comprehensive text focuses on the homotopical technology in use at the forefront of modern algebraic topology. Following on from a standard introductory algebraic topology sequence, it will provide students with a comprehensive background in spectra...

This genuine introduction to the differential geometry of plane curves is designed as a first text for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. The book assumes only foundational year...

The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal method for the resolution of a class of singularities in algebraic geometry. At the same...

Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, fractal geometry, conformal dynamics, discrete groups, geometric group theory, algebraic curves and their moduli, various kinds of deformation...

The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of...

Poisson geometry lies at the cusp of noncommutative algebra and differential geometry, with natural and important links to classical physics and quantum mechanics. This book presents an introduction to the subject from a small group of leading...

The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This 1997 book presents an introductory account of the subject in the style of the original discoverers, with...

The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology,...

The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems. They succinctly cover an unparalleled range of topics from the basic concepts of symplectic and...

This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Moebius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford...

This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but...

In this Tract Professor Moreno develops the theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of algebraic geometric Goppa codes on algebraic curves. Amongst the applications considered are:...

This is a self-contained and systematic account of affine differential geometry from a contemporary view, not only covering the classical theory, but also introducing more modern developments. In order both to cover as much as possible and to keep the...

Finite geometry and combinatorics is the art of counting any phenomena that can be described by a diagram. Everyday life is full of applications; from telephones to compact disc players, from the transmission of confidential information to the codes on...

This volume is based on lectures given at a workshop and conference on symplectic geometry at the University of Warwick in August 1990. The area of symplectic geometry has developed rapidly in the past ten years with major new discoveries that were...

The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors cast the theory into a new light, that of singularity theory. This second edition has been thoroughly revised...