Groups of homotopy classes : rank formulas and homotopy-commutativity
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 ũy) of homotopy classes of homotopy equivalences of a s...
Salvato in:
| Autori principali: | , |
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| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Heidelberg :
Springer Berlin
2013.
Cham : Springer International Publishing |
| Serie: | Lecture notes in mathematics
4 |
| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Groups of homotopy classes, rank formulas and homotopy-commutativity, M. Arkowitz, C. R. Curjel,..., 1964, Berlin, Springer-Verlag, 1 vol. (36 p.), Lecture notes in mathematics, 0-387-03900-7 |
| Riassunto: | 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 ũy) of homotopy classes of homotopy equivalences of a space Y with itself. The groups [A,nX] and ũY) 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,nũ ũ[A,nx] induced by maps f: A ũB. We prove a general theorem on the rank of the intersection of coincidence subgroups (Theorem 3. 3)... |
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| Descrizione del documento: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. p. 35-36 de l'édition imprimée |
| ISBN: | 9783662159132 3662159139 |
| Accesso: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |