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...
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| Auteurs principaux: | , |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Heidelberg :
Springer Berlin
2013.
Cham : Springer International Publishing |
| Series: | Lecture notes in mathematics
4 |
| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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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 |
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| 100 | 1 | |a Arkowitz, Martin, |d 1935- | |
| 245 | 1 | 0 | |a Groups of homotopy classes : |b rank formulas and homotopy-commutativity |c M. Arkowitz, C.R. Curjel,... |
| 260 | |a Heidelberg : |b Springer Berlin. | ||
| 260 | |a Cham : |b Springer International Publishing, |c 2013. | ||
| 490 | 0 | |a Lecture notes in mathematics |v 4 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. 35-36 de l'édition imprimée | ||
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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)... | ||
| 650 | |a Groupes d'homotopie | ||
| 650 | |a Homotopie | ||
| 650 | |a Groupes, Théorie des | ||
| 700 | 1 | |a Curjel, Caspar, |d 1931-2017. |4 aut | |
| 776 | 0 | |0 011436395 |t Groups of homotopy classes |o rank formulas and homotopy-commutativity |f M. Arkowitz, C. R. Curjel,... |d 1964 |c Berlin |n Springer-Verlag |p 1 vol. (36 p.) |s Lecture notes in mathematics |z 0-387-03900-7 | |
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