Titlebook: Stable Homotopy Theory; Lectures delivered a J. Frank Adams Book 19641st edition Springer-Verlag Berlin Heidelberg 1964 Division.Homologica

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頭腦冷靜

Book 19641st edition(‘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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Book 19641st editioneory 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

Arb853

Primary operations,uch as the celebrated Steenrod square. I recall that this is a homomorphism . defined for each pair (X,Y) and for all non-negative integers i and n. (H. is to be interpreted as singular cohomology.) The Steenrod square enjoys the following properties:

CREST

Primary operations,ow that a proposed geometric construction is impossible, you have to find a topological invariant which shows the impossibility. Among topological invariants we meet first the homology and cohomology groups, with their additive and multiplicative structure. Afte that we meet cohomology operations, s

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