Groups Of Homotopy Classes
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Groups Of Homotopy Classes
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Author : M. Arkowitz
language : en
Publisher: Springer
Release Date : 2006-12-08
Groups Of Homotopy Classes written by M. Arkowitz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Many of the sets that one encounters in homotopy classification problems have a natural group structure. Among these are the groups [A, nX] of homotopy classes of maps of a space A into a loop-space nx. Other examples are furnished by the groups (̃y) of homotopy classes of homotopy equivalences of a space Y with itself. The groups [A, nX] and (̃Y) are not necessarily abelian. It is our purpose to study these groups using a numerical invariant which can be defined for any group. This invariant, called the rank of a group, is a generalisation of the rank of a finitely generated abelian group. It tells whether or not the groups considered are finite and serves to distinguish two infinite groups. We express the rank of subgroups of [A, nX] and of C(Y) in terms of rational homology and homotopy invariants. The formulas which we obtain enable us to compute the rank in a large number of concrete cases. As the main application we establish several results on commutativity and homotopy-commutativity of H-spaces. Chapter 2 is purely algebraic. We recall the definition of the rank of a group and establish some of its properties. These facts, which may be found in the literature, are needed in later sections. Chapter 3 deals with the groups [A, nx] and the homomorphisms f*: [B, nl̃ ̃[A, nx] induced by maps f: A ̃B. We prove a general theorem on the rank of the intersection of coincidence subgroups (Theorem 3. 3).
Groups Of Homotopy Classes
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Author : M. Arkowitz
language : en
Publisher:
Release Date : 2014-01-15
Groups Of Homotopy Classes written by M. Arkowitz 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.
Groups Of Homotopy Classes
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Author : M. Arkowitz
language : it
Publisher:
Release Date : 1964
Groups Of Homotopy Classes written by M. Arkowitz 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.
Groups Of Homotopy Classes
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Author : M. Arkowitz
language : en
Publisher:
Release Date : 2014-01-15
Groups Of Homotopy Classes written by M. Arkowitz 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.
Groups Of Homotopy Classes Rank Formulas And Homotopy Commutative
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Author : M. Arkowitz
language : en
Publisher:
Release Date : 1967
Groups Of Homotopy Classes Rank Formulas And Homotopy Commutative written by M. Arkowitz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Commutator Calculus And Groups Of Homotopy Classes
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Author : Hans J. Baues
language : en
Publisher: Cambridge University Press
Release Date : 1981-11-05
Commutator Calculus And Groups Of Homotopy Classes written by Hans J. Baues 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 1981-11-05 with Mathematics categories.
A fundamental problem of algebraic topology is the classification of homotopy types and homotopy classes of maps. In this work the author extends results of rational homotopy theory to a subring of the rationale. The methods of proof employ classical commutator calculus of nilpotent group and Lie algebra theory and rely on an extensive and systematic study of the algebraic properties of the classical homotopy operations (composition and addition of maps, smash products, Whitehead products and higher order James-Hopi invariants). The account is essentially self-contained and should be accessible to non-specialists and graduate students with some background in algebraic topology and homotopy theory.
Groups Of Homotopy Classes
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Author : Martin Arkowitz
language : de
Publisher:
Release Date : 1964
Groups Of Homotopy Classes written by Martin Arkowitz 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.
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.
Composition Methods In Homotopy Groups Of Spheres Am 49 Volume 49
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Author : Hiroshi Toda
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Composition Methods In Homotopy Groups Of Spheres Am 49 Volume 49 written by Hiroshi Toda 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 2016-03-02 with Mathematics categories.
The description for this book, Composition Methods in Homotopy Groups of Spheres. (AM-49), Volume 49, will be forthcoming.
Groups Of Homotopy Spheres I
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Author : M. A. Kervaire
language : en
Publisher:
Release Date : 2023-07-18
Groups Of Homotopy Spheres I written by M. A. Kervaire and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with History categories.