Localization Of Nilpotent Groups And Spaces
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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.
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.
Localization In Group Theory And Homotopy Theory And Related Topics
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Author : P.J. Hilton
language : en
Publisher: Springer
Release Date : 2006-11-15
Localization In Group Theory And Homotopy Theory And Related Topics written by P.J. Hilton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Algebraic Topology New Trends In Localization And Periodicity
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Author : Carles Broto
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Algebraic Topology New Trends In Localization And Periodicity written by Carles Broto 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.
Central to this collection of papers are new developments in the general theory of localization of spaces. This field has undergone tremendous change of late and is yielding new insight into the mysteries of classical homotopy theory. The present volume comprises the refereed articles submitted at the Conference on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. Several comprehensive articles on general localization clarify the basic tools and give a report on the state of the art in the subject matter. The text is therefore accessible not only to the professional mathematician but also to the advanced student.
Crystallographic Groups And Their Generalizations
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Author : Paul Igodt
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Crystallographic Groups And Their Generalizations written by Paul Igodt 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 2000 with Mathematics categories.
This volume contains articles written by the invited speakers and workshop participants from the conference on "Crystallographic Groups and Their Generalizations", held at Katholieke Universiteit Leuven, Kortrijk (Belgium). Presented are recent developments and open problems. Topics include the theory of affine structures and polynomial structures, affine Schottky groups and crooked tilings, theory and problems on the geometry of finitely generated solvable groups, flat Lorentz 3-manifolds and Fuchsian groups, filiform Lie algebras, hyperbolic automorphisms and Anosov diffeomorphisms on infra-nilmanifolds, localization theory of virtually nilpotent groups and aspherical spaces, projective varieties, and results on affine appartment systems. Participants delivered high-level research mathematics and a discussion was held forum for new researchers. The survey results and original papers contained in this volume offer a comprehensive view of current developments in the field.
Homological Localization Towers For Groups And Pi Modules
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Author : A. K. Bousfield
language : en
Publisher: American Mathematical Soc.
Release Date : 1977
Homological Localization Towers For Groups And Pi Modules written by A. K. Bousfield 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 1977 with Mathematics categories.
This paper investigates algebraic homological localizations which have arisen in the homotopy theoretic study of localizations of spaces. It focuses on the "HR-localization" of groups and the "HZ localization" of modules over a group [capital Greek]Pi, where the coefficient ring [italic]R is allowed to be a subring of the rationals or a finite cyclic ring. The investigation is based on a construction of natural transfinite towers which eventually stabilize to the desired homological localizations. These towers are used to show that the HR-local groups form the smallest class of groups containing the trivial group, closed under inverse limits, and closed under central [italic]R-module extensions.
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.
Localization And Cohomology Of Nilpotent Groups
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Author : Peter J. Hilton
language : en
Publisher:
Release Date : 1973
Localization And Cohomology Of Nilpotent Groups written by Peter J. Hilton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
Algebraic Topology
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Author : Jaume Aguade
language : en
Publisher: Springer
Release Date : 2006-11-15
Algebraic Topology written by Jaume Aguade and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The papers in this collection, all fully refereed, original papers, reflect many aspects of recent significant advances in homotopy theory and group cohomology. From the Contents: A. Adem: On the geometry and cohomology of finite simple groups.- D.J. Benson: Resolutions and Poincar duality for finite groups.- C. Broto and S. Zarati: On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C. Ravenel: Morava K-theories of classifying spaces and generalized characters for finite groups.- K. Ishiguro: Classifying spaces of compact simple lie groups and p-tori.- A.T. Lundell: Concise tables of James numbers and some homotopyof classical Lie groups and associated homogeneous spaces.- J.R. Martino: Anexample of a stable splitting: the classifying space of the 4-dim unipotent group.- J.E. McClure, L. Smith: On the homotopy uniqueness of BU(2) at the prime 2.- G. Mislin: Cohomologically central elements and fusion in groups.
Aspects Of Infinite Groups
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Author : Benjamin Fine
language : en
Publisher: World Scientific
Release Date : 2008
Aspects Of Infinite Groups written by Benjamin Fine and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book is a festschrift in honor of Professor Anthony Gaglione''s sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.