Lie algebras and vn-periodic spaces

• 成果类型: Article
• 署名作者: Heuts, Gijs
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2021.193.1.3
• 发表日期: 2021
• 页码: 223-301
• 关键词: upsilon-1-periodic homotopy-groups; goodwillie tower; COHOMOLOGY; HOMOLOGY; localization; complexes

摘要

We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in v(n)-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen's results in the rational case, we prove that this v(n)-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in T(n)-local spectra. We also compare it to the homotopy theory of commutative coalgebras in T(n)-local spectra, where it turns out there is only an equivalence up to a certain convergence issue of the Goodwillie tower of the identity.