Algebraic topology

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The papers in this collection, all fully refereed, originalpapers, reflect many aspects of recent significant advancesin homotopy theory and group cohomology.

Historical interest and studies of Weyl's role in the interplay between 20th-century mathematics, physics and philosophy have been increasing since the middle 1980s, triggered by different activities at the occasion of the centenary of his birth in 1985, and are far from being exhausted.

Were I to take an iron gun, And ?

As the interaction of mathematics and theoretical physics continues to intensify, the theories developed in mathematics are being applied to physics, and conversely.

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 textbook provides a succinct introduction to algebraic topology.

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.

This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory.

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

This book serves as a textbook in real analysis.

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

Algebraic Topology is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years.

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

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

In this second edition, the following recent papers have been added: "e;Gauss Codes, Quantum Groups and Ribbon Hopf Algebras"e;, "e;Spin Networks, Topology and Discrete Physics"e;, "e;Link Polynomials and a Graphical Calculus"e; and "e;Knots Tangles and Electrical Networks"e;.

This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary.

The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics.

The KK-theory of Kasparov is now approximately twelve years old; its power, utility and importance have been amply demonstrated.

This book gives an intuitive and hands-on introduction to Topological Data Analysis (TDA).

With one exception, these papers are original and fullyrefereed research articles on various applications ofCategory Theory to Algebraic Topology, Logic and ComputerScience.

The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory.

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

This book is an introduction to modern methods of symplectic topology.

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.

This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds.

The homology of manifolds enjoys a remarkable symmetry: Poincare duality.

This book is a new edition of "e;Tensors and Manifolds: With Applications to Mechanics and Relativity"e; which was published in 1992.

A NATO Advanced Study Institute entitled "e;Algebraic K-theory and Algebraic Topology"e; was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991.

Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory.

An elementary introduction to homology theory suitable for undergraduate courses or for self-study.

Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics.

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

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

This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values.

The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds.

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 includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths.

Introduction In the last few years a few monographs dedicated to the theory of topolog- ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM].

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

This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory.

This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the "e;Higher homotopical structures"e; programme.

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

This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property.

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.