Book Description

From the reviews: "This volume... consists of two papers. The first, written by V.V. Shokurov, is devoted to the theory of Riemann surfaces and algebraic curves. It is an excellent overview of the theory of relations between Riemann surfaces and their models - complex algebraic curves in complex projective spaces. ... The second paper, written by V.I. Danilov, discusses algebraic varieties and schemes. ... I can recommend the book as a very good introduction to the basic algebraic geometry." European Mathematical Society Newsletter, 1996 "... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." Acta Scientiarum Mathematicarum ... Read more

Book Description

Proceedings of the third International Symposium on Hamiltonian Systems and Celestial Mechanics, held in Patzcuaro, Michoacan, Mexico, December 7-11, 1998. Topics covered by the talks included Arnold diffusion, central configurations, area preserving maps, and billiards. ... Read more

Book Description

Together with the authors' Volume I. C*-Theory, the two parts comprising Functional Differential Equations: II. C*-Applications form a masterful work-the first thorough, up-to-date exposition of this field of modern analysis lying between differential equations and C*-algebras. The two parts of Volume II contain the applications of the C*-structures and theory developed in Volume I. They show the technique of using the C*-results in the study of the solvability conditions of non-local functional differential equations and demonstrate the fundamental principles underlying the interrelations between C* and functional differential objects. The authors focus on non-local pseudodifferential, singular integral, and Toeplitz operators-with continuous and piecewise continuous coefficients-convolution type operators with oscillating coefficients and shifts, and operators associated with non-local boundary value problems containing transformation operators of an argument on the boundary. They build the symbolic calculus for all these classes of operators, use it to treat concrete examples of non-local operators, present the explicit computation of their Fredholmity conditions and the index formulae, and obtain a number of related results.Part 1: Equations with Continuous Coefficients and Part 2: Equations with Discontinuous Coefficients and Boundary Value Problems can each stand alone and prove a valuable resource for researchers and students interested in operator algebraic methods in the theory of functional differential equations, and to pure C*-algebraists looking for important and promising new applications. Together these books form a powerful library for this intriguing field of modern analysis. ... Read more

Book Description

This is a book on topological graph theory written from a purely combinatorial viewpoint. The aim is to develop a rigorous approach to the foundations of the subject. The book should therefore appeal to graduate students and researchers in topological graph theory. The basic tool used is the idea of a 3-graph which is a cubic graph endowed with a proper edge colouring in three colours. A special case of a 3-graph, called a gem, provides a model for a cellular imbedding of a graph in a surface. Thus theorems about imbeddings of graphs become theorems about gems. In the book we show that many of these theorems generalise to theorems about 3-graphs. ... Read more

Book Description

In this book, the author develops a generative theory of shape with two properties fundamental to intelligence: maximizing transfer of structure, and maximizing recoverability of generative operations. The theory is applied in considerable detail to CAD, perception, and robotics. A significant aspect of this book is the development of an object-oriented theory of geometry. This includes a group-theoretic formulation of object-oriented inheritance. In particular, a class of groups is developed called "unfolding groups", which define any complex shape as unfolded from a maximally collapsed version of itself called an "alignment kernel". The group is decomposed into levels corresponding to the inheritance hierarchy within the complex object. This achieves one of the main goals of the theory - the conversion of complexity into understandability. The advantages of the theory are demonstrated with lengthy studies of robot manipulators, perceptual organization, constructive solid geometry, assembly planning, architectural CAD, and mechanical CAD/CAM. ... Read more

Book Description

This research note presents a complete treatment of the connection between topological circle planes and topological generalized quadrangles. The author uses this connection to provide a better understanding of the relationships between different types of circle planes and to solve a topological version of the problem of Apollonius. Topological Circle Planes and Topological Quadrangles begins with a foundation in classical circle planes and the real symmetric generalized quadrangle and the connection between them. This provides a solid base from which the author offers a more generalized exploration of the topological case. He also compares this treatment to the finite case. Subsequent chapters examine Laguerre, Möbius, and Minkowski planes and their respective relationships to antiregular quadrangles. The author addresses the Lie geometry of each and discuss the relationships of circle planes-the "sisters" of Möbius, Laguerre, and Minkowski planes - and concludes by solving a topological version of the problem of Apollonius in Laguerre, Möbius, and Minkowski planes.The treatment offered in this volume offers complete coverage of the topic. The first part of the text is accessible to anyone with a background in analytic geometry, while the second part requires basic knowledge in general and algebraic topology. Researchers interested in geometry-particularly in topological geometry-will find this volume intriguing and informative. Most of the results presented are new and can be applied to various problems in the field of topological circle planes.Features ... Read more

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Hardbound. ... Read more

Book Description

Knot theory is the study of embeddings of circles in space. Peter Cromwell has written a textbook on knot theory designed for use in advanced undergraduate or beginning graduate-level courses. The exposition is detailed and careful yet engaging and full of motivation. Numerous examples and exercises serve to help students through the material, while an instructor's manual is available online. ... Read more

Book Description

This research-level monograph on harmonic maps between singular spaces sets out much new material on the theory, bringing all the research together for the first time in one place. Riemannian polyhedra are a class of such spaces that are especially suitable to serve as the domain of definition for harmonic maps. Their properties are considered in detail, with many examples being given, and potential theory on Riemmanian polyhedra is also considered. The work will serve as a concise source and reference for all researchers working in this field or a similar one. ... Read more

Book Description

This book is based on a graduate course taught by the author at the University of Maryland.The lecture notes have been revised and augmented by examples. The first two chapters develop the elementary theory of Artin Braid groups, both geometrically and via homotopy theory, and discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem. The final two chapters give a detailed investigation of polynomial covering maps, which may be viewed as a homomorphism of the fundamental group of the base space into the Artin Braid group on n strings. ... Read more

Book Description

This monograph offers a broad investigative tool in ergodic theory and measurable dynamics.The motivation for this work is that one may measure how similar two dynamical systems are by asking how much the time structure of orbits of one system must be distorted for it to become the other. Different restrictions on the allowed distortion will lead to different restricted orbit equivalence theories. These include Ornstein's Isomorphism theory, Kakutani Equivalence theory and a list of others. By putting such restrictions in an axiomatic framework, a general approach is developed that encompasses all of these examples simultaneously and gives insight into how to seek further applications. ... Read more

Book Description

Hardbound. This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.

Key features:

• More terms from General Topology than any other book ever published
• Short and informative articles
• Authors include the majority of top researchers in the field
• Extensive indexing of terms ... Read more

Book Description

Foremost experts in their field have contributed articles resulting in a compilation of useful and timely surveys in this ever-expanding field. Each of these 12 original papers covers important aspects of design theory including several in areas that have not previously been surveyed. Also contains surveys updating earlier ones where research is particularly active. ... Read more

Reviews (1)

A MUST HAVE for the design theorist
This book is an excellent collection of survey articles that spans the breadth of design theory.This book, in addition to the CRC Handbook of Combinatorial Designs should be on every design theorist's shelf. ... Read more

Book Description

The focus of this book is on combinatorial objects, dessins d'enfants, which are drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action of the absolute Galois group on them. The articles contained here unite basic elements of the subject with recent advances. Topics covered include: the explicity association of algebraic curves to dessins, the study of the action of the Galois group on the dessins, computation and combinatorics, relations with modular forms, geometry, generating functions, TeichmÜller and moduli spaces.Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book. ... Read more

Book Description

The main aim of this text is to introduce the beginner to thetheory of topological rings. Whilst covering all the essential theoryof topological groups, the text focuses on locally compact, compact,linearly compact, hereditarily linear compact and bounded topologicalrings. The text also contains new, unpublished results on topological rings,for example the nilideals of topological rings, trivial extensions ofspecial type, rings with a unique compact topology, compact righttopological rings and the results from groups of units of topologicalrings. ... Read more

Book Description

Hardbound. This is a comprehensive introduction into the method of inverse spectra - a powerful method successfully employed in various branches of topology.

The notion of an inverse sequence and its limits, first appeared in the well-known memoir by Alexandrov where a special case of inverse spectra - the so-called projective spectra - were considered. The concept of an inverse spectrum in its present form was first introduced by Lefschetz. Meanwhile, Freudental, had introduced the notion of a morphism of inverse spectra. The foundations of the entire method of inverse spectra were laid down in these basic works.

Subsequently, inverse spectra began to be widely studied and applied, not only in the various major branches of topology, but also in functional analysis and algebra. This is not surprising considering the categorical nature of inverse spectra and the extraordinary power of the related techniques.

Updated surveys (including proofs of sever ... Read more

Book Description

The Surveys in Differential Geometry are supplements to the Journal of Differential Geometry, which are published by International Press. They include significant invited papers combining original research and overviews of the most current research in specific areas of interest to the growing Journal of Differential Geometry community.The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers. These supplements are published annually since 1999.

This volume arises out of the conference sponsored by the Journal of Differential Geometry and held at Harvard University to honor the four mathematicians who founded Index Theory. A large number of geometers gathered for this historic occasion which included numerous tributes and reminiscences which will be published in a separate volume. The four founders of the Index Theory - Michael Atiyah, Raoul Bott, Frederich Hirzebruch, and Isadore Singer - are sources of inspiration, mentors and teachers for the other speakers and participants at the conference. The larger-than-usual size of this volume derives directly from the tremendous respect and admiration for the honorees. ... Read more

Reviews (1)

Be At One With The Topological Cosmos
I used this textbook to supplement Dr. Cain's notes in a topology class at Georgia Tech.I found it to be an excellent introduction to the subject.Theorems are proved with clarity, and the exercises inspire thought about the subject matter.This book was the first place I encountered a proof of the Tychonoff Product Theorem. The proof was presented very well, in my opinion.In addition, there is no shortage of examples in each section.I would heartily recommend this book to anyone with an interest in learning general topology. ... Read more