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:
- 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)
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