Topology 21

This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic co……続きを見る

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical app……続きを見る

This monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplec……続きを見る

This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manif……続きを見る

This textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable. Rich in examples, exercises and motivation, it provides a careful and clear exposition at……続きを見る

This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a si……続きを見る

This book introduces the reader to the most important concepts and problems in the field of ℓ²-invariants. After some foundational material on group von Neumann algebras, ℓ²-Betti numbers are define……続きを見る

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 subject has been studied intensively, s……続きを見る

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with th……続きを見る

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations t……続きを見る

This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances……続きを見る

This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms. One main theme i……続きを見る

This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions o……続きを見る

This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provi……続きを見る

This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is compr……続きを見る

This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designe……続きを見る

This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in d……続きを見る

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the ……続きを見る

An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is to provide a refe……続きを見る

This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of suc……続きを見る

This second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree ……続きを見る

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to ……続きを見る

An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces……続きを見る

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. He had just received the Fiel……続きを見る

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers ……続きを見る

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. In cases where the conjecture is known t……続きを見る

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 cha……続きを見る

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The ……続きを見る

This textbook offers a uniquely accessible introduction to flows on compact surfaces, filling a gap in the existing literature. The book can be used for a single semester course and/or for independe……続きを見る

This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category ……続きを見る