Lectures On Homotopy Theory
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Lectures On Homotopy Theory
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Author : R.A. Piccinini
language : en
Publisher: Elsevier
Release Date : 1992-01-21
Lectures On Homotopy Theory written by R.A. Piccinini and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-21 with Mathematics categories.
The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps. Later, the book was expanded to introduce CW-complexes and their homotopy groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity.
Lectures On Homotopy Theory
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Author : Renzo A. Piccinini
language : en
Publisher: Elsevier
Release Date : 1992-01-01
Lectures On Homotopy Theory written by Renzo A. Piccinini and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the n th homotopy group of the sphere S n, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of S n are trivial and that the third homotopy group of S 2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations (rather thoroughly), simplicial structures and the homotopy groups of maps. groups, to construct a special class of CW-complexes (the Eilenberg-Mac Lane spaces) and to include a chapter devoted to the study of the action of the fundamental group on the higher homotopy groups and the study of fibrations in the context of a category in which the fibres are forced to live; the final material of that chapter is a comparison of various kinds of universal fibrations. Completing the book are two appendices on compactly generated spaces and the theory of colimits. The book does not require any prior knowledge of Algebraic Topology and only rudimentary concepts of Category Theory are necessary; however, the student is supposed to be well at ease with the main general theorems of Topology and have a reasonable mathematical maturity.
Lectures On Algebraic Topology
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Author : Haynes R Miller
language : en
Publisher: World Scientific
Release Date : 2021-09-20
Lectures On Algebraic Topology written by Haynes R Miller and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Mathematics categories.
Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
Stable Homotopy Theory
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Author : J.F. Adams
language : en
Publisher: Springer
Release Date : 2013-11-11
Stable Homotopy Theory written by J.F. Adams and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Homotopy Theory And Models
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Author : Marc Aubry
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Homotopy Theory And Models written by Marc Aubry 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.
In keeping with the general aim of the "D.M.V.-Seminar" series, this book is princi pally a report on a group of lectures held at Blaubeuren by Professors H. J. Baues, S. Halperin and J.-M. Lemaire, from October 30 to November 7, 1988. These lec tures were devoted to providing an introduction to the theory of models in algebraic homotopy. The three lecturers acted in concert to produce a coherent exposition of the theory. Commencing from a common starting point, each of them then proceeded naturally to his own subject of research. The reader who is already familiar with their scientific work will certainly give the lecturers their due. Having been asked by the speakers to take on the responsibility of writing down the notes, it seemed to me that the material elucidated in the short span of fifteen hours was too dense to appear, unedited, in book form. Some amplification was necessary. Of course I submitted to them the final version of this book, which received their approval. I thank them for this token of confidence. I am also grateful to all three for their help and advice in writing this book. I am particularly indebted to J.-M. Lemaire who was indeed very often consulted. For basic notions (in particular those concerning homotopy groups, CW complexes, (co)homology and homological algebra) the reader is advised to refer to the fundamental books written by E. H. Spanier [47], R. M. Switzer [49] and G. Whitehead [52].
Stable Homotopy And Generalised Homology
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Author : John Frank Adams
language : en
Publisher: University of Chicago Press
Release Date : 1974
Stable Homotopy And Generalised Homology written by John Frank Adams 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 1974 with Mathematics categories.
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Stable Homotopy Theory Lectures Delivered At The Univ Of California At Berkeley 1961
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Author : John Frank Adams
language : en
Publisher:
Release Date : 1964
Stable Homotopy Theory Lectures Delivered At The Univ Of California At Berkeley 1961 written by John Frank Adams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
Combinatorial And Toric Homotopy Introductory Lectures
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Author : Darby Alastair
language : en
Publisher: World Scientific
Release Date : 2017-10-20
Combinatorial And Toric Homotopy Introductory Lectures written by Darby Alastair and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-20 with Mathematics categories.
This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis–Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students. Contents: Toric Homotopy Theory (Stephen Theriault)Fullerenes, Polytopes and Toric Topology (Victor M Buchstaber and Nikolay Yu Erokhovets)Around Braids (Vladimir Vershinin)Higher Limits, Homology Theories and fr-Codes (Sergei O Ivanov and Roman Mikhailov)Configuration Spaces and Robot Motion Planning Algorithms (Michael Farber)Cellular Stratified Spaces (Dai Tamaki) Readership: Advanced undergraduate and graduate students as well as researchers interested in homotopy theory and its applications in the sciences. Keywords: Toric Topology;Toric Homotopy;Configuration Space;Stratified Spaces;Braid Group;Fullerene;Polytope;Virtual Braid Group;Thompson Group;Robotics;Motion PlanningReview: Key Features: The first book in the area of toric homotopy theory consisting of introductory lectures on the topics and their applications to fr-codes and robot motion planning
Homotopy Theory And Models
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Author : Marc Aubry
language : en
Publisher:
Release Date : 1995-03-27
Homotopy Theory And Models written by Marc Aubry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-27 with categories.
This book is based upon notes taken by the author at the DMV Seminar on Algebraic Models of Homotopy Types led by H.J. Baues, S. Halperin and J.-M. Lemaire in 1988. The notes have been substantially reorganized and expanded for this publication and now include some additional important proofs. The aim of the work is to provide an overview of homotopy theory from the point of view of algebraic models of homotopy types, leading the reader from the basic definitions in algebraic topology to specific fields of research. The exposition is directed towards graduate students as well as researchers from other fields. Due to the scope and size of this book, only a few complete proofs could be given. But the fundamental concepts and methods of the subject are pointed out, and a number of recent results are included together with the essential bibliographic references. The text begins with a review of the basic notions of homotopy theory. An extensive discussion of rational homotopy theory, emphasizing both the Sullivan and the Quillen models, follows. Next, the Adams-Hilton and the Anick models are shown to yield some integral information. The last chapter gives an introduction to the integral classification of homotopy types, along the lines initiated by J.H.C. Whitehead and considerably developed by H. Baues during the last decade.
Stable Homotopy Theory
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Author : J. Frank Adams
language : en
Publisher: Springer
Release Date : 1964
Stable Homotopy Theory written by J. Frank Adams and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Mathematics categories.
Before I get down to the business of exposition, I'd like to offer a little motivation. I want to show that there are one or two places in homotopy theory where we strongly suspect that there is something systematic going on, but where we are not yet sure what the system is. The first question concerns the stable J-homomorphism. I recall that this is a homomorphism J: ~ (SQ) ~ ~S = ~ + (Sn), n large. r r r n It is of interest to the differential topologists. Since Bott, we know that ~ (SO) is periodic with period 8: r 6 8 r = 1 2 3 4 5 7 9· . · Z o o o z On the other hand, ~S is not known, but we can nevertheless r ask about the behavior of J. The differential topologists prove: 2 Th~~: If I' = ~ - 1, so that 'IT'r(SO) ~ 2, then J('IT'r(SO)) = 2m where m is a multiple of the denominator of ~/4k th (l\. being in the Pc Bepnoulli numher.) Conject~~: The above result is best possible, i.e. J('IT'r(SO)) = 2m where m 1s exactly this denominator. status of conJectuI'e ~ No proof in sight. Q9njecture Eo If I' = 8k or 8k + 1, so that 'IT'r(SO) = Z2' then J('IT'r(SO)) = 2 , 2 status of conjecture: Probably provable, but this is work in progl'ess.