000 | 03356nam a22004815i 4500 | ||
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001 | 978-3-662-15913-2 | ||
003 | DE-He213 | ||
005 | 20190213151602.0 | ||
007 | cr nn 008mamaa | ||
008 | 130628s1964 gw | s |||| 0|eng d | ||
020 |
_a9783662159132 _9978-3-662-15913-2 |
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024 | 7 |
_a10.1007/978-3-662-15913-2 _2doi |
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_aMAT000000 _2bisacsh |
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_aPB _2thema |
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_a510 _223 |
100 | 1 |
_aArkowitz, M. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aGroups of Homotopy Classes _h[electronic resource] : _bRank formulas and homotopy-commutativity / _cby M. Arkowitz, C. R. Curjel. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1964. |
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300 |
_aIII, 36 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v4 |
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505 | 0 | _aGroups of finite rank -- The Groups [A,?X] and Their Homomorphisms -- Commutativity and Homotopy-Commutativity -- The Rank of the Group of Homotopy Equivalences. | |
520 | _aMany 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). | ||
650 | 0 | _aMathematics. | |
650 | 1 | 4 |
_aMathematics, general. _0http://scigraph.springernature.com/things/product-market-codes/M00009 |
700 | 1 |
_aCurjel, C. R. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662159156 |
776 | 0 | 8 |
_iPrinted edition: _z978A54000515 |
776 | 0 | 8 |
_iPrinted edition: _z9783662159149 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v4 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-662-15913-2 |
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912 | _aZDB-2-LNM | ||
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_c11188 _d11188 |