Algebraic topology

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

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiri Matousek, who passed away prematurely in March 2015.

Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices.

Explains both the how and the why of linear algebra to get students thinking like mathematicians.

This introduction to braid groups keeps prerequisites to a minimum, while discussing their rich mathematical properties and applications.

Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places.

This book constitutes a review volume on the relatively new subject of Quantum Topology.

Several recent investigations have focused attention on spaces and manifolds which are non-compact but where the problems studied have some kind of "e;control near infinity"e;.

Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters.

The physical properties of knotted and linked configurations in space have long been of interest to mathematicians.

The NATO Advanced Study Institute on "e;The Arithmetic and Geometry of Algebraic Cycles"e; was held at the Banff Centre for Conferences in Banff (Al- berta, Canada) from June 7 until June 19, 1998.

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

This book grew out of courses which I taught at Cornell University and the University of Warwick during 1969 and 1970.

This book is a first sketch of what the overall field of performance could look like as a modern scientific field but not its stylistically differentiated practice, pedagogy, and history.

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

This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra.

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

This volume consists of ten lectures given at an international workshop/conference on knot theory held in July 1996 at Waseda University Conference Center.

An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

Some Historical Background This book deals with the cohomology of groups, particularly finite ones.

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks.

Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology.

Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.

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

Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context.

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.

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.

In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities.

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.

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.

This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology.

Uses the combinatorics and representation theory to construct and study important families of Lie algebras and Weyl groups.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.

This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology.

An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.

A bend is a knot securely joining together two lengths of cord (or string or rope), thereby yielding a single longer length.

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

The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry.

In this book we consider deep and classical results of homotopy theory like the homological Whitehead theorem, the Hurewicz theorem, the finiteness obstruction theorem of Wall, the theorems on Whitehead torsion and simple homotopy equivalences, and we characterize axiomatically the assumptions under which such results hold.

This lecture notes volume presents significant contributions from the "e;Algebraic Geometry and Number Theory"e; Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014.

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