Multiplicative structure of finite ring spectra and stable homotopy of spheres
Multiplicative structure of finite ring spectra and stable homotopy of spheres
复制标题
DOI：
10.1007/bfb0075582
复制
发表时间：
1984
期刊：
影响因子：
--
通讯作者：
Shichirô Oka
中科院分区：
文献类型：
--
作者：
Shichirô Oka
在本文中，p用p5表示一个素数。本文在比较一般的情况下，证明了球的稳定同伦群在t维上有任意多个p-初级产生元。对于s1 [14J]，存在一个具有s - BP-同调BP*{Ks)= BP*/(p, vi)的4元环谱K，当s= 0时，它具有k1 \K分裂成4个Ks s [15J]副本的性质。我们称这样分裂的K为分裂环谱。我们在[15 J]中的结果是由分裂环谱K的稳定自映射（即S = 0 mod p的K）构造而成的，并且它们在Adams-Novikov的e2项的ext2中被检测到。
Throughout this paper, p will denote a prime with p 5. In this paper, we develope ideas, in somewhat general situation, with which we have proved [15] that the stable homotopy group of spheres, has arbitrarily many p-primary generators in dimension t for sufficiently large t. There is a 4-cell ring spectrum K with s BP-homology BP*{Ks)= BP*/(p, vi) for s 1 [14J, and if s= 0 mod pit has a property that K 1\K splits into four copies of Ks s s [15J. We cal1ed K with such splitting a split ring spectrum. The S s. generators of* an our results in [15 J are constructed from stable self-maps of split ring spectra K, ie, K with s= 0 mod p, and s s they are detected in Ext2of Adams-Novikov'· s E2term.