Groups of Homotopy Classes : Rank formulas and homotopy-commutativity. 1st ed. 1964

種類:

電子ブック

責任表示:

by M. Arkowitz, C.R. Curjel

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1964

著者名:

• Arkowitz, M.
• Curjel, C.R.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 4

ISBN:

9783662159132 [3662159139]    

注記:

Groups of finite rank -- The Groups [A,?X] and Their Homomorphisms -- Commutativity and Homotopy-Commutativity -- The Rank of the Group of Homotopy Equivalences.
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

ローカル注記:

学内専用E-BOOKS (local access only)