Topology

A comprehensive, self-contained treatment presenting general results of the theory.

The essentials of point-set topology, complete with motivation and numerous examples Topology: Point-Set and Geometric presents an introduction to topology that begins with the axiomatic definition of a topology on a set, rather than starting with metric spaces or the topology of subsets of Rn.

This is the first self-contained exposition of the connections between symbolic dynamical systems, dimension groups and Bratteli diagrams.

This timely text introduces topological data analysis from scratch, with detailed case studies.

This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.

A collection of research papers, both new and expository, based on the interests of Professor J.

This introduction to braid groups keeps prerequisites to a minimum, while discussing their rich mathematical properties and applications.

Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.

Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.

A complete and definitive account of the authors'' resolution of the Kervaire invariant problem in stable homotopy theory.

The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.

Friendly introduction to higher index theory, a growing subject at the intersection of geometry, topology and operator algebras.

In this graduate-level book, leading researchers explore various new notions of ''space'' in mathematics.

In this graduate-level book, leading researchers explore various new notions of ''space'' in mathematical physics.

Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.

This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.

Complete account of a new classification of connected Lie groups in two classes, including open problems to motivate further study.

An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications.

Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications.

Represents the state of the art in the new field of synthetic differential topology.

A comprehensive introduction to stable homotopy theory for beginning graduate students, from motivating phenomena to current research.

Presents the current state of knowledge in all aspects of two-dimensional homotopy theory.

At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

A leading expert presents a unified concept of slenderness in Abelian categories, with numerous open problems and exercises.

A step-by-step guide to Langlands'' early work leading up the Langlands Program for mathematicians and advanced students.

Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.

With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.

Concise and modern introduction to differential topology with a hands-on approach and plentiful examples and exercises.

A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.

Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Concise and modern introduction to differential topology with a hands-on approach and plentiful examples and exercises.

The first systematic account of the basic theory of normed algebras, without assuming associativity.

Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.

An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Surveys the state of the art in geometric and cohomological group theory.

Details some of the most recent developments at the interface of topology and geometric group theory.

Detailed account of analysis on Polish spaces with a straightforward introduction to optimal transportation.

Detailed account of analysis on Polish spaces with a straightforward introduction to optimal transportation.

A self-contained exposition of local class field theory for students in advanced algebra.

A self-contained exposition of local class field theory for students in advanced algebra.

The first of two volumes covering the Steenrod algebra and its various applications.

The second of two volumes covering the Steenrod algebra and its various applications.

A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.