Topology Books

Historically, applications of algebraic topology to the study of topological transformation groups were originated in the work of L. E. 1. Brouwer on periodic transformations and, a little later, in the beautiful fixed point...

The object of this book is a presentation of the major results relating to two geometrically inspired problems in analysis. One is that of determining which metric spaces can be isometrically embedded in a Hilbert space or,...

An ultrafilter is a truth-value assignment to the family of subsets of a set, and a method of convergence to infinity. From the first (logical) property arises its connection with two-valued logic and model theory; from the...

Topological Dynamics has its roots deep in the theory of differential equations, specifically in that portion called the "qualitative theory". The most notable early work was that of Poincare and Bendixson, regarding stability...

This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor...

General topology is the domain ofmathematics devoted to the investigation of the concepts of continuity and passage to a limit at their natural level of generality. The most basic concepts of general topology, that of a...

This book presents Maslov's canonical operator method for finding asymptotic solutions of pseudo differential equations. The classical WKB method, so named in honor of its authors: Wentzel, Kramers and Brillouin, was created...

In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its...

This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade. The author...

This book constitutes the proceedings of the 4th International Workshop on Computational Topology in Image Context, CTIC 2012, held in Bertinoro, Italy, in May 2012. The 16 papers presented in this volume were carefully...

The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the...

The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot...

Hamiltonian Equations.- to the KAM Theory.- Splitting of Asymptotic Manifolds.- The Separatrix Map.- Width of the Stochastic Layer.- The Continuous Averaging Method.- The Anti-Integrable Limit.- Hill's Formula.

This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and...

Manifolds.- Topology of Riemann Surfaces.- Analytic Structure.- Diffierentials and Integration.- Tori and Jacobians.- Projective Varieties.- Moduli Spaces of Curves.- Vector Bundles, Sheaves and Cohomology.- The Theorem of Riemann-Roch for Line Bundles.-...

A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects...

Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified...

From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction...

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the...

This reference work deals with important topics in general topology and their role in functional analysis and axiomatic set theory, for graduate students and researchers working in topology, functional analysis, set theory and...

An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics...

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder [40] and Laumon [62]. In writing this text based on a...

This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students...

With applications in mind, this self-contained monograph provides a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres, making the subject accessible to researchers and graduates with a...

This book is devoted to applications of singularity theory in mathematics and physics, covering a broad spectrum of topics and problems. "The book contains a huge amount of information from all the branches of Singularity...

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf...

Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of...

The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic...

The Set Theory and Applications meeting at York University, Ontario, featured both contributed talks and a series of invited lectures on topics central to set theory and to general topology. These proceedings contain a...

These proceedings include selected and refereed original papers; most are research papers, a few are comprehensive survey articles.

The book is the second part of an intended three-volume treatise on semialgebraic topology over an arbitrary real closed field R. In the first volume (LNM 1173) the category LSA(R) or regular paracompact locally semialgebraic...

This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's...

The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic...

This volume is a collection of papers dedicated to the memory of V. A. Rohlin (1919-1984) - an outstanding mathematician and the founder of the Leningrad topological school. It includes survey and research papers on topology of...

The first part of this research monograph discusses general properties of G-ENRBs - Euclidean Neighbourhood Retracts over B with action of a compact Lie group G - and their relations with fibrations, continuous submersions, and...

The contributions making up this volume are expanded versions of the courses given at the C.I.M.E. Summer School on the Theory of Moduli.

The book gives a systematic exposition of the diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered include: constructions and...

Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of...

Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the...

This book seeks to construct a consistent fundamental quantum theory of gravity, which is often considered one of the most challenging open problems in present-day physics. It approaches this challenge using modern functional renormalization group...

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. In this book the authors observe that it also occurs in natural phenomena of all scales: 1-dimensional surgery happens during DNA recombination and when...

In this thesis, the author develops numerical techniques for tracking and characterising the convoluted nodal lines in three-dimensional space, analysing their geometry on the small scale, as well as their global fractality and topological...

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents...