Topology

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

This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania).

This monograph presents an approachable proof of Mirzakhani's curve counting theorem, both for simple and non-simple curves.

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 book provides an introduction to deformation quantization and its relation to quantum field theory, with a focus on the constructions of Kontsevich and Cattaneo & Felder.

This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids.

This textbook provides a succinct introduction to algebraic topology.

This volume is devoted to various aspects of Alexandrov Geometry for those wishing to get a detailed picture of the advances in the field.

This book provides a comprehensive survey of the Sharkovsky ordering, its different aspects and its role in dynamical systems theory and applications.

This book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point.

This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication.

This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.

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 textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable.

This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps.

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 presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances.

This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas.

The volume consists of a set of surveys on geometry in the broad sense.

The book addresses the minimization of special lower semicontinuous functionals over closed balls in metric spaces, called the approximate variation.

This book comprises an overview of twelve months of intense activity of the research group Geometry, Topology, Algebra, and Applications (GEOMVAP) at the Universitat Politecnica de Catalunya (UPC).

This book provides an introduction to some key subjects in algebra and topology.

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 is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nykoping, Sweden.

This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams.

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology.

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 is the second volume of the Handbook of the Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.

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.

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry.

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 is devoted to computing the index of elliptic PDEs on non-compact Riemannian manifolds in the presence of local singularities and zeros, as well as polynomial growth at infinity.

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

This book presents, in a clear and structured way, the set function \mathcal{T} and how it evolved since its inception by Professor F.

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis.

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.

This book delivers stimulating input for a broad range of researchers, from geographers and ecologists to psychologists interested in spatial perception and physicists researching in complex systems.

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the study of scalar curvature rigidity and positive mass theorems using spinors and the Dirac operator It is intended for both graduate students and researchers.

This book consists of 16 surveys on Thurston's work and its later development.

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces.

This book is the first systematic treatment of this area so far scattered in a vast number of articles.

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.

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory.

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.