The Adams-Novikov E 2 -Term for a Complex with p Cells
The Adams-Novikov E 2 -Term for a Complex with p Cells
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DOI：
10.2307/2374362
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发表时间：
1985-08
影响因子：
1.7
通讯作者：
D. Ravenel
中科院分区：
文献类型：
--
作者：
D. Ravenel
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where each attaching map between adjacent cells is a,1 E rqt (S0). X is also the skeleton of a certain Thom spectrum T(1) of a bundle over QSq+I to be described below. The details of extracting -x* (SO) from -x* (X) will be described elsewhere. Our description of the latter is simple enough to be intelligible and to convince the casual reader of its probable accuracy. For p 5 our range of dimensions is new. Nakamura-Oka [4] has computed irk(S?) for k s (2p2 + 4p + l)q 6 and Aubry [2] has computed it for k ? (3p2 + 4p)q 1. We will compute the E2-term of the Adams-Novikov spectral sequence (ANSS) for i-* (X). It will follow for trivial reasons that there are no nontrivial differentials or group extensions in our range. We can describe our result briefly. E"t for s = 0, 1 for X are closely related to the corresponding groups for So which are well known (see [3]). E2t is known for the sphere and is generated by the elements fi3j,' sE2,q(P+l)i-qj where i > 0 and j = 1 unless p I i in which case 1 c j c p. With the exception of (31 these elements all have nontrivial images in E 2t for X. To describe the rest of E2 we need some notation. Let P(1) be the Hopf algebra Z/(p)[t1, t2]/(t Pj, t'P) with dim ti = 2(pi 1), t1 is primitive and t2 = t2 t8 1 + tI (g t'pi + 1 (g t2. P(t) is dual to the subalgebra of the mod(p) Steenrod algebra generated by Pl and PP.