Adams filtration and generalized Hurewicz maps for infinite loopspaces

• 成果类型: Article
• 署名作者: Kuhn, Nicholas J.
• 署名单位: University of Virginia
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0814-0
• 发表日期: 2018
• 页码: 957-998
• 关键词: model categories; HOMOLOGY; functors; COHOMOLOGY; calculus; SPACES

摘要

We study the Hurewicz map is the generalized homology theory associated to a connective commutative S-algebra R. We prove that the decreasing filtration of the domain associated to an R-based Adams resolution is compatible with a filtration of the range associated to the augmentation ideal filtration of the augmented commutative S-algebra. The proof of our main theorem makes much use of composition properties of this filtration and its interaction with Topological Andre-Quillen homology. An application is a Connectivity Theorem: localize away from is finite. We illustrate these theorems with calculations of the mod 2 Hurewicz image of BO, its connected covers, and is now given the Adams-Novikov filtration.