Topology

Traditionally, knot theory deals with diagrams of knots and the search of invariants of diagrams which are invariant under the well known Reidemeister moves.

This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Cech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory.

Graduate students and researchers in applied mathematics, optimization, engineering,  computer science, and  management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization.

This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in interesting new directions.

A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.

This book presents the interplay between topological Markov shifts and Cuntz–Krieger algebras by providing notations, techniques, and ideas in detail.

This book presents a systematic and comprehensive account of the theory of differentiable manifolds and provides the necessary background for the use of fundamental differential topology tools.

This book combines a detailed exposition of the basics of fusion systems with a survey of the current state of the field.

A comprehensive introduction to stable homotopy theory for beginning graduate students, from motivating phenomena to current research.

This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Rado.

Visionary articles explaining approaches to important problems on the interface of pure mathematics and mathematical physics.

An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: * Differential Topology * Mathematical Economics * Dynamical Systems * Theory of Computation * Nonlinear Functional Analysis * Physical and Biological Applications This book comprises the proceedings of that conference.

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces.

"e;Descriptive Topology in Selected Topics of Functional Analysis"e; is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis.

This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances.

This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations.

Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.

Up-to-date research in metric diffusion along compact foliations is presented in this book.

The contributions in this volume-dedicated to the work and mathematical interests of Oleg Viro on the occasion of his 60th birthday-are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap among analysis, geometry, and topology.

This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances.

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.

Geomodeling applies mathematical methods to the unified modeling of the topology, geometry, and physical properties of geological objects.

High-dimensional knot theory is the study of the embeddings of n-dimensional manifolds in (n+2)-dimensional manifolds, generalizing the traditional study of knots in the case n=1.

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This book contains selected chapters on recent research in topology.

This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.

A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed.

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 volume presents some of the longstanding research problems of Geometry and Topology.

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal.

This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article.

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An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi–Grothendieck theory of dessins d''enfants.

A graduate-level introduction to finite classical groups featuring a comprehensive account of the conjugacy and geometry of elements of prime order.

This monograph presents a short course in computational geometry and topology.

This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids.

This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought.

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

This volume originated in the workshop held at Nagoya University, August 28-30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set.

These proceedings reflect the main activities of the Paris Seminaire d'Algebre 1989-1990, with a series of papers in Invariant Theory, Representation Theory and Combinatorics.

The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings.

A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized.

Four-Dimensional Manifolds and Projective Structure may be considered first as an introduction to di?