Algebraic topology

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

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Godel's Theorem, and the Skolem Paradox.

This volume contains the original lecture notes presented by A.

The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces.

This book is dedicated to the structure and combinatorics of classical Hopf algebras.

This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology).

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.

This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process.

In Chapter 6, we describe the concept of braid equivalence from the topological point of view.

These proceedings reflect the main activities of the Paris Seminaire d'Algebre 1989-1990, with a series of papers in Invariant Theory, Representation Theory and Combinatorics.

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure written for students.

Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties.

This volume contains the Notes of a seminar on Intersection Ho- logy which met weekly during the Spring 1983 at the University of Bern, Switzerland.

This book contains some important new contributions to the theory of structured ring spectra.

This book is primarily concerned with the study of cohomology theories of general topological spaces with "e;general coefficient systems.

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

Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories.

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory.

A leading expert presents a unified concept of slenderness in Abelian categories, with numerous open problems and exercises.

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

This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmuller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018.

First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English.

This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Cech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory.

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 volume presents some of the longstanding research problems of Geometry and Topology.

Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition.

This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015.

The book addresses a key question in topological field theory and logarithmic conformal field theory: In the case where the underlying modular category is not semisimple, topological field theory appears to suggest that mapping class groups do not only act on the spaces of chiral conformal blocks, which arise from the homomorphism functors in the category, but also act on the spaces that arise from the corresponding derived functors.

This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples.

This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics.

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations.

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.

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

The first authored book to present the mathematical foundations and applications of this exciting new field.

This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds.

This concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H.

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015.

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R.

A comprehensive introduction to stable homotopy theory for beginning graduate students, from motivating phenomena to current research.

This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis.

In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications.

This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline.

An authoritative introduction to the essential features of etale cohomologyA.