"Group theory." . . "Algebra homológica." . . "Groupes d'homotopie." . . "Groups. Theory of." . . "Grups d'homotopia." . . "Représentations de groupes." . . "Mathématiques." . . . . "Homotopia, Teoría de." . . "SpringerLink (Service en ligne)" . . "Homotopia" . . "Homotopia." . "groupe homotopie." . . "Théorie des groupes." . . "Groupes abéliens." . . "Gruppentheorie." . . "Semi-groupes." . . "Teoria de grups" . . "Teoria de grups." . "Homotopy theory." . . "homomorphisme." . . "Homotopy groups." . . "Homotopiegruppe." . . "Homotopieklasse." . . "Grupos de homotopia." . . "Grupos de homotopía." . "Grupos de classes (Matematica)" . . "Homotopie." . . "homotopie." . "Groups of homotopy classes Rank formulas and homotopy-commutativity" . . . . . . . . "Groups of homotopy classes : (rank formulas and homotopy commutativity)" . . . . . "Groups of homotopy classes : (rank formulas and homotopy-commutativity)" . "Groups of homotopy classes; rank formulas and homotopy-commutativity" . "Groups of homotopy classes; rank formulas and homotopy-commutativity"@en . . . . . . . . "Groups of homotopy classes : (Rank formulas and homotopy-commutativity)" . . . "Llibres electrònics" . . . . . . . . . . . . . . . . . . . . . . . . . "Groups of homotopy classes : Rank formulas and homotopy-commutativity" . . . . . . . . "Groups of homotopy classes" . "Groups of homotopy classes"@en . . . . . "Groups of homotopy classes : rank formulas and homotopy"@en . "Groups of homotopy classes rank formulas and homotopy-commutativity" . "Groups of homotopy classes rank formulas and homotopy - commutativity" . . "Groups of homotopy classes rank formulas and homotopy-commutativity"@en . "Groups of homotopy classes : (Rank formulas and homotopy-commutativity.)" . . . . . . . . "Groups of homotopy classes : rank formulas and homotopy-commutativity" . . "Groups of homotopy classes : rank formulas and homotopy-commutativity"@en . . . . . . . . . . . . . . . "Groups of Homotopy Classes : Rank formulas and homotopy-commutativity" . . . . . . "Groups of Homotopy Classes (Rank formulas and Homotopy-commutativity)" . . "Groups of Homotopy Classes Rank formulas and homotopy-commutativity" . "Electronic books"@en . "Electronic books" . "Groups of Homotopy Classes"@it . "Groups of Homotopy Classes" . "Groups of Homotopy Classes"@en . . . . . . . . . . . "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 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)."@en . "Springer-Verlag." . . "Algebrai topológia." . . "Homotópiaelmélet." . . "commutativité." . . "Gruppi di omotopia." . . "Teoria grup." . . "Homotopia Grups." . . "équivalence homotopie." . . "Topologie." . . "Groupes, Théorie des." . .