Topology

Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space.

A comprehensive account giving advanced students and researchers an accessible route into the wide-ranging field of differential topology.

A NATO Advanced Study Institute entitled "e;Algebraic K-theory and Algebraic Topology"e; was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991.

This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds.

Optimal Solution of Nonlinear Equations is a text/monograph designed to provide an overview of optimal computational methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mapping, and for the computation of the topological degree.

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory.

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the study of scalar curvature rigidity and positive mass theorems using spinors and the Dirac operator It is intended for both graduate students and researchers.

An elementary introduction to homology theory suitable for undergraduate courses or for self-study.

Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics.

This book is a comprehensive treatment of the theory of persistence modules over the real line.

Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction.

This book discusses key conceptual aspects and explores the connection between triangulated manifolds and quantum physics, using a set of case studies ranging from moduli space theory to quantum computing to provide an accessible introduction to this topic.

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This book deals with the new class of one-dimensional variational problems - the problems with branching solutions.

This monograph presents a new model of mathematical structures called weak n-categories.

This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values.

For this printing of R.

The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds.

Authoritative and comprehensive account; an essential handbook for all those working in the area.

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites.

Probability limit theorems in infinite-dimensional spaces give conditions un- der which convergence holds uniformly over an infinite class of sets or functions.

The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory.

Hellmuth Kneser (1898-1973) ist der Zweite von drei bedeutenden Mathematikern aus aufeinander folgenden Generationen der Familie Kneser, die wegweisende Erkenntnisse in einem erstaunlich breiten Spektrum von Spezialgebieten beisteuerten.

This volume includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths.

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

A lucid and self-contained treatment of many key ideas in topological dynamics, achieved by focusing on equivalence relations and automorphisms.

Introduction In the last few years a few monographs dedicated to the theory of topolog- ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM].

This monograph could be used for a graduate course on symplectic geometry as well as for independent study.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.

This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory.

This book is devoted to the structure of the Mandelbrot set - a remarkable and important feature of modern theoretical physics, related to chaos and fractals and simultaneously to analytical functions, Riemann surfaces, phase transitions and string theory.

Emphasizes topological, geometrical and analytical properties of absolute measurable spaces; of interest for real analysis, set theory and measure theory.

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader.

Many nonlinear problems in physics, engineering, biology and social sciences can be reduced to finding critical points of functionals.

This book develops methods which explore some new interconnections and interrelations between Analysis and Topology and their applications.

This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the "e;Higher homotopical structures"e; programme.

This book is dedicated to the structure and combinatorics of classical Hopf algebras.

An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.

In kurzer und prägnanter Form wird die Analysis der Grundvorlesung vorgestellt.

Presents the current state of knowledge in all aspects of two-dimensional homotopy theory.

This book delivers stimulating input for a broad range of researchers, from geographers and ecologists to psychologists interested in spatial perception and physicists researching in complex systems.

This work is suitable for undergraduate students as well as advanced students and research workers.

This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property.