Topology

This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut.

Topology is the mathematical study of the most basic geometrical structure of a space.

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves.

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves.

Topology is the mathematical study of the most basic geometrical structure of a space.

The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces.

The Poincar Conjecture tells the story behind one of the world s most confounding mathematical theories.

Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research.

This textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable.

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(R^d,n) from its beginnings to recent developments.

This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere.

This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three.

This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators.

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives.

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory.

Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses.

This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas.

Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research.

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions.

This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure.

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications.

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces.

This book provides a comprehensive and up-to-date introduction to Hodge theory-one of the central and most vibrant areas of contemporary mathematics-from leading specialists on the subject.

I have intended this book to be more than just the sum of its chapters, and the introduction is, in part, an attempt to spell out what the more is.

North-Holland Mathematical Library, Volume 26: Shape Theory: The Inverse System Approach presents a systematic introduction to shape theory by providing background materials, motivation, and examples, including shape theory and invariants, pro-groups, shape fibrations, and metric compacta.

The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade.

These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s.

Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets.

This classic work has been fundamentally revised to take account of recent developments in general topology.

The first part of this book is a text for graduate courses in topology.

In this book we study function spaces of low Borel complexity.

Two types of seemingly unrelated extension problems are discussed in this book.

This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians.

Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments.

The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers.

This monograph presents developments in the abstract theory of topological dynamics, concentrating on the internal structure of minimal flows (actions of groups on compact Hausdorff spaces for which every orbit is dense) and their homomorphisms (continuous equivariant maps).

The first edition of this monograph appeared in 1978.

An Introduction to Homological Algebra discusses the origins of algebraic topology.

This volume of the Mathematics Studies presents work done on composition operators during the last 25 years.

This text brings the reader to the frontiers of current research in topological rings.

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This book is an introduction to the theory of knots via the theory of braids, which attempts to be complete in a number of ways.

Some Applications of Topological K-Theory

This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c).

The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared.

This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction.

Applications from condensed matter physics, statistical mechanics and elementary particle theory appear in the book.

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces.

Aimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction.