| 书目名称 | Stable Homotopy Theory | | 副标题 | Lectures delivered a | | 编辑 | J. Frank Adams | | 视频video | | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | 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. | | 出版日期 | Book 19641st edition | | 关键词 | Division; Homological algebra; Homotopie; Homotopy; Morphism; behavior; homomorphism; homotopy theory; proof | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-15942-2 | | isbn_ebook | 978-3-662-15942-2Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 1964 |
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发表于 2025-3-21 17:38:05
