Algebraic topology

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

This book is based on notes for a master's course given at Queen Mary, University of London, in the 1998/9 session.

Shape theory is an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces.

In the first volume of this survey (Arnol'd et al.

This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck  theorem.

This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology.

This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra.

This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects.

This book is based on lectures I have given to senior undergraduate and graduate audiences at Oxford and elsewhere over the years.

This book, the third book in the four-volume series in algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology.

Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form.

This text introduces students to an experimental approach to mathematics, using Maple to systematically investigate and develop mathematical theory.

The second of two volumes offering a modern account of Kaehlerian geometry and Hodge theory for researchers in algebraic and differential geometry.

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds.

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications.

This book is an introduction to manifolds at the beginning graduate level.

This book is an introduction to the role of topology in the quantization of classical systems.

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

Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.

Real analytic sets in Euclidean space (Le.

This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus.

This is the third version of a book on differential manifolds.

The second of two volumes covering the Steenrod algebra and its various applications.

A-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of earlier works of Sugawara's homotopy characterization of H-spaces and loop spaces.

A comprehensive treatment of Floer homology, based on the Seiberg–Witten equations, first published in 2007.

In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day.

This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.

This volume is the Proceedings of the Third Korea-China-Japan Inter- national Symposium on Ring Theory held jointly with the Second Korea- Japan Joint Ring Theory Seminar which took place at the historical resort area of Korea, Kyongju, June 28-July 3, 1999.

This book serves as a textbook in real analysis.

We dedicate this book to the memory of J.

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

Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie.

Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences.

Fields-medal winner Donaldson reviews current work, including his own, on the theory of Floer.

Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces.

Central to this collection of papers are new developments in the general theory of localization of spaces.

The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s.

Differential and complex geometry are two central areas of mathematics with a long and intertwined history.

Algebraic K-Theory has become an increasingly active area of research.