Homotopy Limits Completions And Localizations
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Homotopy Limits Completions And Localizations
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Author : A. K. Bousfield
language : en
Publisher: Springer
Release Date : 2009-03-20
Homotopy Limits Completions And Localizations written by A. K. Bousfield and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-20 with Mathematics categories.
The main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X. For R=Zp and X subject to usual finiteness condition, the R-completion coincides up to homotopy, with the p-profinite completion of Quillen and Sullivan; for R a subring of the rationals, the R-completion coincides up to homotopy, with the localizations of Quillen, Sullivan and others. In part II of these notes, the authors have assembled some results on towers of fibrations, cosimplicial spaces and homotopy limits which were needed in the discussions of part I, but which are of some interest in themselves.
Homotopy Limits Completions And Localizations
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Author : Aldridge Knight Bousfield
language : en
Publisher: Springer Verlag
Release Date : 1972
Homotopy Limits Completions And Localizations written by Aldridge Knight Bousfield and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Algebra, Homological. categories.
Homotopy Limits Completions And Localizations
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Author : A. K. Bousfield
language : en
Publisher:
Release Date : 2014-01-15
Homotopy Limits Completions And Localizations written by A. K. Bousfield and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
More Concise Algebraic Topology
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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 2012-02
More Concise Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02 with Mathematics categories.
With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.
Categorical Homotopy Theory
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Author : Emily Riehl
language : en
Publisher: Cambridge University Press
Release Date : 2014-05-26
Categorical Homotopy Theory written by Emily Riehl 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 2014-05-26 with Mathematics categories.
This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.
Localization Of Nilpotent Groups And Spaces
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Author : Peter Hilton
language : en
Publisher: Elsevier
Release Date : 2016-06-03
Localization Of Nilpotent Groups And Spaces written by Peter Hilton and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.
North-Holland Mathematics Studies, 15: Localization of Nilpotent Groups and Spaces focuses on the application of localization methods to nilpotent groups and spaces. The book first discusses the localization of nilpotent groups, including localization theory of nilpotent groups, properties of localization in N, further properties of localization, actions of a nilpotent group on an abelian group, and generalized Serre classes of groups. The book then examines homotopy types, as well as mixing of homotopy types, localizing H-spaces, main (pullback) theorem, quasifinite nilpotent spaces, localization of nilpotent complexes, and nilpotent spaces. The manuscript takes a look at the applications of localization theory, including genus and H-spaces, finite H-spaces, and non-cancellation phenomena. The publication is a vital source of data for mathematicians and researchers interested in the localization of nilpotent groups and spaces.
Cohomological Methods In Homotopy Theory
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Author : Jaume Aguade
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Cohomological Methods In Homotopy Theory written by Jaume Aguade 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.
This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matemtica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category. The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.
Stable And Unstable Homotopy
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Author : William G. Dwyer
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-01-01
Stable And Unstable Homotopy written by William G. Dwyer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
This volume presents the proceedings of workshops on stable homotopy theory and on unstable homotopy theory held at The Fields Institute as part of the homotopy program during the year 1996. The papers in the volume describe current research in the subject, and all included works were refereed. Rather than being a summary of work to be published elsewhere, each paper is the unique source for the new material it contains. The book contains current research from international experts in the subject area, and presents open problems with directions for future research.
Adams Memorial Symposium On Algebraic Topology Volume 2
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Author : Nigel Ray
language : en
Publisher: Cambridge University Press
Release Date : 1992-05-07
Adams Memorial Symposium On Algebraic Topology Volume 2 written by Nigel Ray 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 1992-05-07 with Mathematics categories.
J. Frank Adams had a profound influence on algebraic topology, and his work continues to shape its development. The International Symposium on Algebraic Topology held in Manchester during July 1990 was dedicated to his memory, and virtually all of the world's leading experts took part. This two volume work constitutes the proceedings of the symposium; the articles contained here range from overviews to reports of work still in progress, as well as a survey and complete bibliography of Adam's own work. These proceedings form an important compendium of current research in algebraic topology, and one that demonstrates the depth of Adams' many contributions to the subject. This second volume is oriented towards homotopy theory, the Steenrod algebra and the Adams spectral sequence. In the first volume the theme is mainly unstable homotopy theory, homological and categorical.
The Grothendieck Festschrift Volume Iii
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Author : Pierre Cartier
language : en
Publisher: Springer
Release Date : 2007-10-23
The Grothendieck Festschrift Volume Iii written by Pierre Cartier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-23 with Mathematics categories.
This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.