Algebraic topology

Homological algebra first arose as a language for describing topological prospects of geometrical objects.

Jürgen Beetz führt zuerst in den Ursprung der erdachten Geschichten der Mathematik aus der Steinzeit ein.

This unique book offers an introductory course on category theory, which became a working language in algebraic geometry and number theory in the 1950s and began to spread to logic and computer science soon after it was created.

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

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface.

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This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere.

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.

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 proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015.

MATRIX is Australia's international, residential mathematical research institute.

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

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.

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.

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.

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings.

This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples.

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.

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

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

This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory.

This book is the fifth and final volume of Raoul Bott's Collected Papers.

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives.

Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries.

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.

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

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.

This book is a comprehensive treatment of the theory of persistence modules over the real line.

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.

This book constitutes the proceedings of the 6th International Workshop on Computational Topology in Image Context, CTIC 2016, held in Marseille, France, in June 2016.

Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras.

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces.

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.

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.

The second edition of this highly praised textbook provides an expanded introduction to the theory of ordered sets and its connections to various subjects.

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 textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I.

This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role.

The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "e;Conference on Geometric Analysis"e; (thirteen abstracts) and at the "e;Conference on Type Theory, Homotopy Theory and Univalent Foundations"e; (seven abstracts), both held at the Centre de Recerca Matematica (CRM) in Barcelona from July 1st to 5th, 2013, and from September 23th to 27th, 2013, respectively.

The topic of this book sits at the interface of the theory of higher categories (in the guise of (infinity,1)-categories) and the theory of properads.

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

This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach.

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.

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

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory.

This Volume presents a unified approach to calculate the plane stress distribution of stress and strain in thin elastic/plastic discs subject to various loading conditions.

This monograph presents theoretical methods involving the Hamilton-Jacobi-Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control.