Algebraic topology

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

This volume (a sequel to LNM 1108, 1214, 1334 and 1453)continues the presentation to English speaking readers ofthe Voronezh University press series on Global Analysis andIts Applications.

A small conference was held in September 1986 to discuss new applications of elliptic functions and modular forms in algebraic topology, which had led to the introduction of elliptic genera and elliptic cohomology.

The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity.

The D(2) problem is a fundamental problem in low dimensional topology.

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

This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example.

The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry.

This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators.

This volume gathers the contributions from the international conference "e;Intelligence of Low Dimensional Topology 2006,"e; which took place in Hiroshima in 2006.

Permutation Groups form one of the oldest parts of group theory.

This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018.

Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.

An advanced treatment of surgery theory for graduate students and researchersSurgery theory, a subfield of geometric topology, is the study of the classifications of manifolds.

This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis.

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.

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

Contains a combination of selected papers given in honour of John Frank Adams which illustrate the profound influence that he had on algebraic topology.

Plurisubharmonic functions playa major role in the theory of functions of several complex variables.

Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions.

Manifolds fall naturally into two classes depending on whether they can be fitted with a distance measuring function or not.

This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author.

This popular graduate text has been thoroughly revised and updated to incorporate recent developments in the field.

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds.

This text brings the reader to the frontiers of current research in topological rings.

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These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980.

This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra.

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

This book brings together twenty essays on diverse topics in the history and science of knots.

This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry.

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field.

Group cohomology has a rich history that goes back a century or more.

This book offers a concise introduction to ergodic methods in group homology, with a particular focus on the computation of L2-Betti numbers.

The Hauptvermutung is the conjecture that any two triangulations of a poly- hedron are combinatorially equivalent.

A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory.

This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998).

'Homology' as a concept became increasingly elusive during the course of the 20th century.

The subject matter of compact groups is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics.

In this book the authors describe the important generalization of the original Weil conjectures, as given by P.

An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming.

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.

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.

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