| 000 | 03249nam a22004695i 4500 | ||
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| 001 | 978-3-662-15942-2 | ||
| 003 | DE-He213 | ||
| 005 | 20190213151143.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 130730s1964 gw | s |||| 0|eng d | ||
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_a9783662159422 _9978-3-662-15942-2 |
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| 024 | 7 |
_a10.1007/978-3-662-15942-2 _2doi |
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_aPBP _2bicssc |
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_aMAT038000 _2bisacsh |
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_aPBP _2thema |
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| 082 | 0 | 4 |
_a514 _223 |
| 100 | 1 |
_aAdams, J. Frank. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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| 245 | 1 | 0 |
_aStable Homotopy Theory _h[electronic resource] / _cby J. Frank Adams. |
| 264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1964. |
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| 300 |
_aIII, 77 p. 3 illus. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v3 |
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| 505 | 0 | _a1. Introduction -- 2. Primary operations. (Steenrod squares, Eilenberg-MacLane spaces, Milnor’s work on the Steenrod algebra.) -- 3. Stable homotopy theory. (Construction and properties of a category of stable objects.) -- 4. Applications of homological algebra to stable homotopy theory. (Spectral sequences, etc.) -- 5. Theorems of periodicity and approximation in homological algebra -- 6. Comments on prospective applications of 5, work in progress, etc. | |
| 520 | _aBefore I get down to the business of exposition, I'd like to offer a little motivation. I want to show that there are one or two places in homotopy theory where we strongly suspect that there is something systematic going on, but where we are not yet sure what the system is. The first question concerns the stable J-homomorphism. I recall that this is a homomorphism J: ~ (SQ) ~ ~S = ~ + (Sn), n large. r r r n It is of interest to the differential topologists. Since Bott, we know that ~ (SO) is periodic with period 8: r 6 8 r = 1 2 3 4 5 7 9· . · Z o o o z On the other hand, ~S is not known, but we can nevertheless r ask about the behavior of J. The differential topologists prove: 2 Th~~: If I' = ~ - 1, so that 'IT"r(SO) ~ 2, then J('IT"r(SO)) = 2m where m is a multiple of the denominator of ~/4k th (l\. being in the Pc Bepnoulli numher.) Conject~~: The above result is best possible, i.e. J('IT"r(SO)) = 2m where m 1s exactly this denominator. status of conJectuI'e ~ No proof in sight. Q9njecture Eo If I' = 8k or 8k + 1, so that 'IT"r(SO) = Z2' then J('IT"r(SO)) = 2 , 2 status of conjecture: Probably provable, but this is work in progl'ess. | ||
| 650 | 0 | _aTopology. | |
| 650 | 1 | 4 |
_aTopology. _0http://scigraph.springernature.com/things/product-market-codes/M28000 |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
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_iPrinted edition: _z9783662159446 |
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_iPrinted edition: _z978A54000513 |
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_iPrinted edition: _z9783662159439 |
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_aLecture Notes in Mathematics, _x0075-8434 ; _v3 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-662-15942-2 |
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