Algebraic topology

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

At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.

The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry.

Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries.

This monograph covers topics in the cohomology of monoids up through recent developments.

The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry.

This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry.

This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories.

Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J.

This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory.

Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems.

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

Algebraic Topology is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years.

The most modern and thorough treatment of unstable homotopy theory available.

Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G.

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

Friendly introduction to higher index theory, a growing subject at the intersection of geometry, topology and operator algebras.

In keeping with the general aim of the "e;D.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Shape and Shape Theory D.

A self-contained exposition of local class field theory for students in advanced algebra.

The main result of this original research monograph is the classification of C*-algebras of ordinary foliations of the plane in terms of a class of -trees.

There have been exciting developments in the area of knot theory in recent years.

The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry.

This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups.

This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties.

The NATO Advanced Study Institute "e;Axiomatic, enriched and rna- tivic homotopy theory"e; took place at the Isaac Newton Institute of Mathematical Sciences, Cambridge, England during 9-20 September 2002.

Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject.

This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry.

Aus den Besprechungen: "Der nunmehr vorliegende zweite Band der Funktionentheorie erfüllt voll die Erwartungen, die der erste Band geweckt hat.

Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups).

This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself.

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 book carefully presents a unified treatment of equivariant Poincare duality in a wide variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere.

The origins of this volume can be traced back to a conference on "e;Ethics, Economic and Business"e; organized by Columbia Busi- ness School in March of 1993, and held in the splendid facilities of Columbia's Casa Italiana.

This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA).

The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics.

This book is a survey of current topics in the mathematical theory of knots.

In this second edition, the following recent papers have been added: "e;Gauss Codes, Quantum Groups and Ribbon Hopf Algebras"e;, "e;Spin Networks, Topology and Discrete Physics"e;, "e;Link Polynomials and a Graphical Calculus"e; and "e;Knots Tangles and Electrical Networks"e;.

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

This book provides the first extensive and systematic treatment of the theory of commutative coherent rings.