Topology Books

This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. 1989 edition.

A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is...

A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general...

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An...

From the very beginning, algebraic topology has developed under the influ­ ence of the problems posed by trying to understand the topological properties of complex algebraic varieties (e.g., the pioneering work by Poincare and...

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are...

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the...

Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. The new edition of this...

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of...

Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds...

The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be accessible to a reader of modest background...

There are many reasons for writing this first volume of strategic activities on fractals. The most pervasive is the compelling desire to provide students of mathematics with a set of accessible, hands-on experiences with...

Many mathematics books suffer from schizophrenia, and this is yet another. On the one hand it tries to be a reference for the basic results on flat riemannian manifolds. On the other hand it attempts to be a textbook which can...

This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential...

This is the first comprehensive book treatment of the emerging subdiscipline of set-valued mapping and enlargements of maximal monotone operators. It features several important new results and applications in the field...

Quite simply, this book offers the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary background material, detailing symmetric and semisymmetric Riemannian manifolds,...

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems,...

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...

Matrix Groups.- Concrete Matrix Groups. The Matrix Exponential Function. Linear Lie Groups. Lie Algebras.- Elementary Structure Theory of Lie Algebras. Root Decomposition. Representation Theory of Lie Algebras.

1 History.- 2 (Topological) Maps.- 3 The Four-Color Theorem (Topological Version).- 4 Topology to Combinatorics.- 5 The Four-Color Theorem (Combinatorial Version).- 6 Reducibility.- 7 The Quest for Unavoidable Sets.- Works of Reference.

Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of...

Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have as- sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics. The three...

Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings. This book deals with the topology of curves...

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but...

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and...

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core...

Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics...

''Intended mainly for physicists and mathematicians...its high quality will definitely attract a wider audience.'' ---Computational Mathematics and Mathematical Physics This work acquaints the physicist with the...

Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of...