Algebraic topology

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

This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry.

This book is based on the lecture notes from a course we taught at Penn State University during the fall of 2002.

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

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

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.

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.

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 study of the geometrical and topological structure of gauge theories.

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 discusses major topics in measure theory, Fourier transforms, complex analysis and algebraic topology.

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

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.

Rational homotopy is a very powerful tool for differential topology and geometry.

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

Nato dall'esperienza dell'autore nell'insegnamento della topologia agli studenti del corso di Laurea in Matematica, questo libro contiene le nozioni fondamentali di topologia generale ed una introduzione alla topologia algebrica.

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout.

Develops a full set of homotopical algebra techniques dedicated to the study of higher categories.

This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets.

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

In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field.

This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold theory.

This textbook on combinatorial commutative algebra focuses on properties of monomial ideals in polynomial rings and their connections with other areas of mathematics such as combinatorics, electrical engineering, topology, geometry, and homological algebra.

One of the most significant unsolved problems in mathematics is the complete classification of knots.

Five years ago, I taught a one-quarter course in homological algebra.

These notes are an expanded and updated version of a course of lectures which I gave at King's College London during the summer term 1979.

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory.

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

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves.

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 rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod.

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties.

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.

The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology.

Electrical, communication, transportation, computer, and neural networks are special kinds of nets.

This book introduces the reader to the most important concepts and problems in the field of l2-invariants.

The first part of this research monograph discusses general properties of G-ENRBs - Euclidean Neighbourhood Retracts over B with action of a compact Lie group G - and their relations with fibrations, continuous submersions, and fibre bundles.

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

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

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 volume of research papers is an outgrowth of the Manin Seminar at Moscow University, devoted to K-theory, homological algebra and algebraic geometry.

Metric and Differential Geometry grew out of a similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing.

The papers collected in this volume are contributions to the 43rd session of the Seminaire ' de mathematiques ' superieures ' (SMS) on "e;Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.