Nonabelian Algebraic Topology
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Nonabelian Algebraic Topology
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Author : Ronald Brown
language : en
Publisher: JP Medical Ltd
Release Date : 2011
Nonabelian Algebraic Topology written by Ronald Brown and has been published by JP Medical Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Algebraic topology categories.
The main theme of this book is that the use of filtered spaces rather than just topological spaces allows the development of basic algebraic topology in terms of higher homotopy groupoids; these algebraic structures better reflect the geometry of subdivision and composition than those commonly in use. Exploration of these uses of higher dimensional versions of groupoids has been largely the work of the first two authors since the mid 1960s. The structure of the book is intended to make it useful to a wide class of students and researchers for learning and evaluating these methods, primarily in algebraic topology but also in higher category theory and its applications in analogous areas of mathematics, physics, and computer science. Part I explains the intuitions and theory in dimensions 1 and 2, with many figures and diagrams, and a detailed account of the theory of crossed modules. Part II develops the applications of crossed complexes. The engine driving these applications is the work of Part III on cubical $\omega$-groupoids, their relations to crossed complexes, and their homotopically defined examples for filtered spaces. Part III also includes a chapter suggesting further directions and problems, and three appendices give accounts of some relevant aspects of category theory. Endnotes for each chapter give further history and references.
Non Abelian Homological Algebra And Its Applications
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Author : Hvedri Inassaridze
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Non Abelian Homological Algebra And Its Applications written by Hvedri Inassaridze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
This book exposes methods of non-abelian homological algebra, such as the theory of satellites in abstract categories with respect to presheaves of categories and the theory of non-abelian derived functors of group valued functors. Applications to K-theory, bivariant K-theory and non-abelian homology of groups are given. The cohomology of algebraic theories and monoids are also investigated. The work is based on the recent work of the researchers at the A. Razmadze Mathematical Institute in Tbilisi, Georgia. Audience: This volume will be of interest to graduate students and researchers whose work involves category theory, homological algebra, algebraic K-theory, associative rings and algebras; algebraic topology, and algebraic geometry.
Topology And Groupoids
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Author : Ronald Brown
language : en
Publisher: Booksurge Llc
Release Date : 2006
Topology And Groupoids written by Ronald Brown and has been published by Booksurge Llc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Annotation. The book is intended as a text for a two-semester course in topology and algebraic topology at the advanced undergraduate orbeginning graduate level. There are over 500 exercises, 114 figures, numerous diagrams. The general direction of the book is towardhomotopy theory with a geometric point of view. This book would providea more than adequate background for a standard algebraic topology coursethat begins with homology theory. For more information seewww.bangor.ac.uk/r.brown/topgpds.htmlThis version dated April 19, 2006, has a number of corrections made.
Homological Algebra
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Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2013-01-11
Homological Algebra written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Mathematics categories.
We propose here a study of ‘semiexact’ and ‘homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied. This is a sequel of a book on ‘Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups’, published by the same Editor, but can be read independently of the latter. The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell — a moderate generalisation of abelian categories that is nevertheless crucial for a theory of ‘coherence’ and ‘universal models’ of (even abelian) homological algebra. The main motivation of the present, much wider extension is that the exact sequences or spectral sequences produced by unstable homotopy theory cannot be dealt with in the previous framework. According to the present definitions, a semiexact category is a category equipped with an ideal of ‘null’ morphisms and provided with kernels and cokernels with respect to this ideal. A homological category satisfies some further conditions that allow the construction of subquotients and induced morphisms, in particular the homology of a chain complex or the spectral sequence of an exact couple. Extending abelian categories, and also the p-exact ones, these notions include the usual domains of homology and homotopy theories, e.g. the category of ‘pairs’ of topological spaces or groups; they also include their codomains, since the sequences of homotopy ‘objects’ for a pair of pointed spaces or a fibration can be viewed as exact sequences in a homological category, whose objects are actions of groups on pointed sets. Homological Algebra: The Interplay of Homology with Distributive Lattices and Orthodox Semigroups Contents:IntroductionSemiexact categoriesHomological CategoriesSubquotients, Homology and Exact CouplesSatellitesUniversal ConstructionsApplications to Algebraic TopologyHomological Theories and Biuniversal ModelsAppendix A. Some Points of Category Theory Readership: Graduate students, professors and researchers in pure mathematics, in particular category theory and algebraic topology. Keywords:Non Abelian Homological Algebra;Spectral Sequences;Distributive Lattices;Orthodox Semigroups;Categories of RelationsReviews: “The range of applications and examples is considerable and many are outside the reach of more standard forms of homological algebra, but the methods used here also give insight as to 'why' the classical theory works and how its results can be interpreted.” Zentralblatt MATH
Algebraic Topology
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Author : Edwin H. Spanier
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Topology written by Edwin H. Spanier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.
Algebraic Topology
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Author : Andrew H. Wallace
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Algebraic Topology written by Andrew H. Wallace and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.
Algebraic Topology
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Author : Clark Bray
language : en
Publisher: Springer Nature
Release Date : 2021-06-18
Algebraic Topology written by Clark Bray and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Mathematics categories.
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. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book begins with the preliminaries needed for the formal definition of a surface. Other topics covered in the book include the classification of surfaces, group theory, the fundamental group, and homology. This book assumes no background in abstract algebra or real analysis, and the material from those subjects is presented as needed in the text. This makes the book readable to undergraduates or high-school students who do not have the background typically assumed in an algebraic topology book or class. The book contains many examples and exercises, allowing it to be used for both self-study and for an introductory undergraduate topology course.
Algebraic Topology
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Author : Allen Hatcher
language : en
Publisher: Cambridge University Press
Release Date : 2002
Algebraic Topology written by Allen Hatcher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.
Simplicial Homotopy Theory
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Author : Paul G. Goerss
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Simplicial Homotopy Theory written by Paul G. Goerss and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
Foundations Of Algebraic Topology
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Author : Samuel Eilenberg
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08
Foundations Of Algebraic Topology written by Samuel Eilenberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.
The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.