On Homotopy Abelian H Spaces

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On Homotopy Abelian H Spaces

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Author : James D. Stasheff
language : en
Publisher:
Release Date : 1961

On Homotopy Abelian H Spaces written by James D. Stasheff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with H-spaces categories.

H Spaces From A Homotopy Point Of View

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Author : James Stasheff
language : en
Publisher: Springer
Release Date : 2006-11-15

H Spaces From A Homotopy Point Of View written by James Stasheff 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 Ten Types Of H Spaces

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Author : I. M. James
language : en
Publisher:
Release Date : 1959

The Ten Types Of H Spaces written by I. M. James and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with H-spaces categories.

Groups Of Homotopy Classes

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Author : M. Arkowitz
language : en
Publisher: Springer
Release Date : 2013-06-29

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 2013-06-29 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,n~l ~ [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).

Abelian Properties Of Anick Spaces

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Author : Brayton Gray
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-02-20

Abelian Properties Of Anick Spaces written by Brayton Gray 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 2017-02-20 with Abelian groups categories.

Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary suspension and enter unstable periodicity. This work describes their -space properties as well as universal properties. Techniques include a new kind on Whitehead product defined for maps out of co-H spaces, calculations in an additive category that lies between the unstable category and the stable category, and a controlled version of the extension theorem of Gray and Theriault (Geom. Topol. 14 (2010), no. 1, 243–275).

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.

Hopf Spaces

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Author :
language : en
Publisher: Elsevier
Release Date : 1976-01-01

Hopf Spaces written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-01-01 with Mathematics categories.

Hopf Spaces

Groups Of Homotopy Classes

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Author : Martin Arkowitz
language : en
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 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,n~l ~ [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).

H Spaces

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Author : Francois Sigrist
language : en
Publisher: Springer
Release Date : 2006-11-15

H Spaces written by Francois Sigrist 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.

Spaces Of Homotopy Self Equivalences A Survey

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Author : John W. Rutter
language : en
Publisher: Springer
Release Date : 2006-11-14

Spaces Of Homotopy Self Equivalences A Survey written by John W. Rutter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

This survey covers groups of homotopy self-equivalence classes of topological spaces, and the homotopy type of spaces of homotopy self-equivalences. For manifolds, the full group of equivalences and the mapping class group are compared, as are the corresponding spaces. Included are methods of calculation, numerous calculations, finite generation results, Whitehead torsion and other areas. Some 330 references are given. The book assumes familiarity with cell complexes, homology and homotopy. Graduate students and established researchers can use it for learning, for reference, and to determine the current state of knowledge.