A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Bmod 2 Cohomology Rings
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A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Bmod 2 Cohomology Rings
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Author : Michael Slack
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Bmod 2 Cohomology Rings written by Michael Slack 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 1991 with Mathematics categories.
Many homological properties of Lie groups are derived strictly from homotopy-theoretic considerations and do not depend on any geometric or analytic structure. An H-space is a topological space having a continuous multiplication with unit. Generalizing from Lie group theory, John Hubbuck proved that a connected, homotopy commutative H-space which is a finite cell complex has the homotopy type of a torus. There are many interesting examples of H-spaces which are not finite complexes - loop spaces are one example. The aim of this book is to prove a version of Hubbuck's theorem in which the condition that the H-space be a finite cell complex is replaced by the condition that it have a finitely-generated mod 2 cohomology ring. The conclusion of the theorem is slightly more general in this case, and some mild associativity hypotheses are required. The method of proof uses established techniques in H-space theory, as well as a new obstruction-theoretic approach to (Araki-Kudo-Dyer-Lashof) homology operations for iterated loop spaces.
A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Mod 2 Cohomology Rings
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Author : Michael Slack
language : en
Publisher:
Release Date : 1991
A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Mod 2 Cohomology Rings written by Michael Slack and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Dyer-Lashof operations categories.
A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Mod 2 Cohomology Rings
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Author : Michael Slack
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
A Classification Theorem For Homotopy Commutative H Spaces With Finitely Generated Mod 2 Cohomology Rings written by Michael Slack 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 1990 with Mathematics categories.
Many homological properties of Lie groups are derived strictly from homotopy-theoretic considerations and do not depend on any geometric or analytic structure. An H-space is a topological space having a continuous multiplication with unit. Generalizing from Lie group theory, John Hubbuck proved that a connected, homotopy commutative H-space which is a finite cell complex has the homotopy type of a torus. There are many interesting examples of H-spaces which are not finite complexes - loop spaces are one example. The aim of this book is to prove a version of Hubbuck's theorem in which the condition that the H-space be a finite cell complex is replaced by the condition that it have a finitely-generated mod 2 cohomology ring. The conclusion of the theorem is slightly more general in this case, and some mild associativity hypotheses are required. The method of proof uses established techniques in H-space theory, as well as a new obstruction-theoretic approach to (Araki-Kudo-Dyer-Lashof) homology operations for iterated loop spaces.
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).
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).
The Homology Of Hopf Spaces
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Author : R.M. Kane
language : en
Publisher: North Holland
Release Date : 1988-08
The Homology Of Hopf Spaces written by R.M. Kane and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-08 with Mathematics categories.
This exposition of the theory of finite Hopf spaces details the development of the subject over the last thirty years, with the homology of such spaces as its main theme. The three chief areas of study in the volume are: - The study of finite H-spaces with torsion free integral homology. - The study of finite H-spaces with homology torsion. - The construction of finite H-spaces.
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.
Groups Of Homotopy Classes
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Author : Martin Arkowitz
language : en
Publisher: Springer
Release Date : 1964
Groups Of Homotopy Classes written by Martin Arkowitz 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 Group theory 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).
Homotopy Type And Homology
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Author : Hans J. Baues
language : en
Publisher: Oxford University Press
Release Date : 1996
Homotopy Type And Homology written by Hans J. Baues and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Research mathematicians in algebraic topology will be interested in this new attempt to classify homotopy types of simply connected CW-complexes. This book provides a modern treatment of a long established set of questions in algebraic topology. The author is a leading figure in this important research area.
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.