The algebra of secondary homotopy operations in ring spectra
نویسندگان
چکیده
منابع مشابه
Ring Spectra via Space - Level Homotopy Theory
Our main goal in this chapter is to show that the spectrum KU representing periodic complex K-theory has an H~ structure. The existence of such a structure is important since it will allow us to develop a complete theory of Dyer-Lashof operations in K-theory, including the computation of K,(O3(); this program is carried out in chapter IX. Of course, we already know that the connective spectrum ...
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This section contains statements of our results on homotopy operations as well as some applications of these results. The proofs depend on material in §2 and will be given in §3Note that, aside from the computations in ~,S at the end of this section, all the results here apply to the homotopy of any H ring spectrum Y. Let ~:DpY + Y denote the structure map. The order of results in this section ...
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Working in the context of symmetric spectra, we describe and study a homotopy completion tower for algebras and left modules over operads in the category of modules over a commutative ring spectrum (e.g., structured ring spectra). We prove a strong convergence theorem that for 0-connected algebras and modules over a (−1)-connected operad, the homotopy completion tower interpolates (in a strong ...
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Homotopy groups of a connective ring spectrum R form an Ngraded algebra π∗R which is commutative if R is commutative. We describe a secondary algebra π∗,∗R which enriches the structure of the algebra π∗R in a new unexpected way. The algebra π∗,∗R encodes secondary homotopy operations in π∗R, such as Toda brackets, and the first Postnikov invariant of R as a ring spectrum. Moreover, π∗,∗R repres...
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In [4] and [6], S. Oka showed that Kr is a ring spectrum for r > 1 if r = 0 (mod p) it is called a split ring spectrum since Kr Λ Kr splits into four summands Kr, ΣKr, Σ r«+ιKr, Σ r«+2Kr. If r φ 0 (mod p), it is called a nonsplit ring spectrum since Krl\Kr splits only into three summands Kr, ΣLΛKr, Σ rq+2Kr, where L is the cofibre of 0i = jaie πrq_χS. In the nonsplit case, S. Oka showed in [4] ...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2010
ISSN: 0024-6115
DOI: 10.1112/plms/pdq034