Algebraic topology

Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces.

This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups.

Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices.

How I have (re-)written this book The book the reader has in hand was supposed to be a new edition of [14].

This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds.

Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology.

The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators.

The book deals with the localization approach to the index problem for elliptic operators.

In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day.

Tamari lattices originated from weakenings or reinterpretations of the familar associativity law.

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

Homotopy theory and C* algebras are central topics in contemporary mathematics.

Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics.

This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean.

This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology.

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

This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds.

This textbook provides a succinct introduction to algebraic topology.

This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community.

This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces.

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(R^d,n) from its beginnings to recent developments.

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

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

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.

This book carefully presents a unified treatment of equivariant Poincare duality in a wide variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere.

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.

This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics.

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

Since the birth of rational homotopy theory, the possibility of extending the Quillen approach -  in terms of Lie algebras - to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community.

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

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

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

The primary aim of this monograph is to achieve part of Beilinson's program on mixed motives using Voevodsky's theories of A1-homotopy and motivic complexes.

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

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

This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions.

This is an in-depth report on the endotrivial modules, an important class of modular representations for finite groups.

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

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

A-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of earlier works of Sugawara's homotopy characterization of H-spaces and loop spaces.

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds.

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