| Dewey Class |
510 |
| Titel |
Groups of Homotopy Classes ([EBook]) : Rank formulas and homotopy-commutativity / by M. Arkowitz, C. R. Curjel. |
| Verfasser |
Arkowitz, Martin. , 1935- |
| Added Personal Name |
Curjel, Caspar Robert , 1931-2017 |
| Other name(s) |
SpringerLink (Online service) |
| Veröffentl |
Berlin, Heidelberg : Springer , 1964. |
| Physical Details |
III, 36 pages : online resource. |
| Reihe |
Lecture Notes in Mathematics, An informal series of special lectures, seminars and reports on mathematical topics 0075-8434 ; ; 4 |
| ISBN |
9783662159132 |
| Summary Note |
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,n~l ~ [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).: |
| Contents note |
Groups of finite rank -- The Groups [A,?X] and Their Homomorphisms -- Commutativity and Homotopy-Commutativity -- The Rank of the Group of Homotopy Equivalences. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-3-662-15913-2 |
| LINKS ZU 'VERWANDTEN WERKEN |
Schlagwörter: .
Group theory .
Homotopy groups .
Homotopy theory .
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