“…This book demonstrates the lively interaction between algebraic topology, very low dimensional topology and combinatorial group theory. …”
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“…The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. …”
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“…Poincaré's papers are in fact the first draft of algebraic topology, introducing its main subject matter (manifolds) and basic concepts (homotopy and homology). …”
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“…Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. …”
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“…In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. …”
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“…Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. …”
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“…It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topology, algebraic/differential geometry, and Lie groups.The first two chapters review differential and integral calculus of several variables and present fundamental results that are used throughout the text. …”
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“…First Definitions Mappings The Separation Axioms Compactness Homeomorphisms Connectedness Path-Connectedness Continua Totally Disconnected Spaces The Cantor Set Metric Spaces Metrizability Baire's Theorem Lebesgue's Lemma and Lebesgue NumbersAdvanced Properties of Topological Spaces Basis and Sub-Basis Product Spaces Relative Topology First Countable, Second Countable, and So ForthCompactifications Quotient Topologies Uniformities Morse Theory Proper Mappings Paracompactness An Application to Digital ImagingBasic Algebraic Topology Homotopy Theory Homology Theory…”
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“…It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.…”
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“…Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. …”
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“…The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. …”
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“…Lefschetz's Topology was written in the period in between the beginning of topology, by Poincaré, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. …”
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“…This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning integral questions and their connections to notions in algebraic topology. This volume features original research articles as well as articles that contain new research and survey some of these recent developments. …”
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“…One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. …”
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“…For many years, algebraic topology rests on three legs: 'ordinary' cohomology, K-theory, and cobordism. …”
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“…The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory.…”
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“…Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. …”
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“…This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. …”
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“…Whitehead, Volume 2: Complexes and Manifolds contains papers that are related in some way to the classification problem for manifolds, especially the Poincare conjecture, but towards the end one sees the gradual transition in the direction of algebraic topology. This volume includes all Whitehead's published work up to the year 1941, as well as a few later papers. …”
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“…It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. …”
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