Algebraic Homotopy PDF Download
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Author | : Hans J. Baues |
Publisher | : Cambridge University Press |
Total Pages | : 490 |
Release | : 1989-02-16 |
Genre | : Mathematics |
ISBN | : 0521333768 |
Download Algebraic Homotopy Book in PDF, ePub and Kindle
This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.
Author | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Download Homotopy Type Theory: Univalent Foundations of Mathematics Book in PDF, ePub and Kindle
Author | : Robert M. Switzer |
Publisher | : Springer |
Total Pages | : 541 |
Release | : 2017-12-01 |
Genre | : Mathematics |
ISBN | : 3642619231 |
Download Algebraic Topology - Homotopy and Homology Book in PDF, ePub and Kindle
From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews
Author | : J. M. Boardman |
Publisher | : Springer |
Total Pages | : 268 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540377999 |
Download Homotopy Invariant Algebraic Structures on Topological Spaces Book in PDF, ePub and Kindle
Author | : Jeffrey Strom |
Publisher | : American Mathematical Society |
Total Pages | : 862 |
Release | : 2023-01-19 |
Genre | : Mathematics |
ISBN | : 1470471639 |
Download Modern Classical Homotopy Theory Book in PDF, ePub and Kindle
The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
Author | : Yves Felix |
Publisher | : Springer Science & Business Media |
Total Pages | : 574 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146130105X |
Download Rational Homotopy Theory Book in PDF, ePub and Kindle
Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago.
Author | : Martin Arkowitz |
Publisher | : Springer Science & Business Media |
Total Pages | : 352 |
Release | : 2011-07-25 |
Genre | : Mathematics |
ISBN | : 144197329X |
Download Introduction to Homotopy Theory Book in PDF, ePub and Kindle
This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts and pullbacks; classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; homotopy Sets; homotopy and homology decompositions of spaces and maps; and obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. The book can be used as a text for the second semester of an advanced ungraduate or graduate algebraic topology course.
Author | : |
Publisher | : Academic Press |
Total Pages | : 383 |
Release | : 1975-11-12 |
Genre | : Mathematics |
ISBN | : 0080873804 |
Download Homotopy Theory: An Introduction to Algebraic Topology Book in PDF, ePub and Kindle
Homotopy Theory: An Introduction to Algebraic Topology
Author | : Tammo tom Dieck |
Publisher | : European Mathematical Society |
Total Pages | : 584 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9783037190487 |
Download Algebraic Topology Book in PDF, ePub and Kindle
This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.
Author | : Fabien Morel |
Publisher | : Springer |
Total Pages | : 267 |
Release | : 2012-07-13 |
Genre | : Mathematics |
ISBN | : 3642295142 |
Download A1-Algebraic Topology over a Field Book in PDF, ePub and Kindle
This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.