Groups of homotopy classes : rank formulas and homotopycommutativity
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The work Groups of homotopy classes : rank formulas and homotopycommutativity represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Groups of homotopy classes : rank formulas and homotopycommutativity
Resource Information
The work Groups of homotopy classes : rank formulas and homotopycommutativity represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Groups of homotopy classes : rank formulas and homotopycommutativity
 Title remainder
 rank formulas and homotopycommutativity
 Statement of responsibility
 M. Arkowitz, C.R. Curjel
 Language
 eng
 Summary
 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 loopspace 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 homotopycommutativity of Hspaces. 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)
 Cataloging source
 SPLNM
 Dewey number
 510.8
 Index
 no index present
 LC call number

 QA611
 QA3
 LC item number
 .L28 no. 4
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Lecture notes in mathematics,
 Series volume
 4
Context
Context of Groups of homotopy classes : rank formulas and homotopycommutativityWork of
 Groups of homotopy classes : rank formulas and homotopycommutativity, M. Arkowitz, C.R. Curjel
 Groups of homotopy classes : rank formulas and homotopycommutativity, M. Arkowitz, C.R. Curjel
 Groups of homotopy classes : rank formulas and homotopycommutativity, M. Arkowitz, C.R. Curjel
 Groups of homotopy classes : rank formulas and homotopycommutativity, M. Arkowitz, C.R. Curjel
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