Stable Homotopy Theory: lectures delivered at the University of California at Berkeley 1961
Before 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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
1964
|
| Schriftenreihe: | Lecture notes in mathematics
3 |
| Schlagworte: | |
| Online-Zugang: | BTU01 UBA01 UBT01 URL des Erstveröffentlichers |
| Zusammenfassung: | Before 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 |
| Beschreibung: | 1 Online-Ressource (III, 77 Seiten) |
| ISBN: | 9783662159422 |
| DOI: | 10.1007/978-3-662-15942-2 |
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| 490 | 1 | |a Lecture notes in mathematics |v 3 | |
| 520 | 3 | |a Before 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 | |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:35:57Z |
| institution | BVB |
| isbn | 9783662159422 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031508649 |
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| spelling | Adams, John Frank 1930-1989 Verfasser (DE-588)120514729 aut Stable Homotopy Theory lectures delivered at the University of California at Berkeley 1961 J. Frank Adams Berlin ; Heidelberg Springer 1964 1 Online-Ressource (III, 77 Seiten) txt rdacontent c rdamedia cr rdacarrier Lecture notes in mathematics 3 Before 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 Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Mathematics Topology Homotopietheorie (DE-588)4128142-1 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 978-3-662-15944-6 Lecture notes in mathematics 3 (DE-604)BV014303148 3 https://doi.org/10.1007/978-3-662-15942-2 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Adams, John Frank 1930-1989 Stable Homotopy Theory lectures delivered at the University of California at Berkeley 1961 Lecture notes in mathematics Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4128142-1 |
| title | Stable Homotopy Theory lectures delivered at the University of California at Berkeley 1961 |
| title_auth | Stable Homotopy Theory lectures delivered at the University of California at Berkeley 1961 |
| title_exact_search | Stable Homotopy Theory lectures delivered at the University of California at Berkeley 1961 |
| title_full | Stable Homotopy Theory lectures delivered at the University of California at Berkeley 1961 J. Frank Adams |
| title_fullStr | Stable Homotopy Theory lectures delivered at the University of California at Berkeley 1961 J. Frank Adams |
| title_full_unstemmed | Stable Homotopy Theory lectures delivered at the University of California at Berkeley 1961 J. Frank Adams |
| title_short | Stable Homotopy Theory |
| title_sort | stable homotopy theory lectures delivered at the university of california at berkeley 1961 |
| title_sub | lectures delivered at the University of California at Berkeley 1961 |
| topic | Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopietheorie |
| url | https://doi.org/10.1007/978-3-662-15942-2 |
| volume_link | (DE-604)BV014303148 |
| work_keys_str_mv | AT adamsjohnfrank stablehomotopytheorylecturesdeliveredattheuniversityofcaliforniaatberkeley1961 |