2019/05/13 by Jens Jakob Kjær, Kjaer, Jens Jakob
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1905.05269
openalex publication_date 2019/05/13 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
In this paper we recover Bousfield's computation of ν1-periodic homotopy groups of simply connected, finite H-spaces from \citeBou99 using the techniques of Goodwillie calculus. This is done through first computing André-Quillen cohomology over the monad \mathbbT that encodes the power operations of complex K-theory. Then lifting this computation to computing K-theory of topological André-Quillen cohomology, and then using results of Behrens and Rezk relating it back to the Bousfield-Kuhn functor. The fact that we recovers the result of Bousfield allows us to conclude ν1-periodic Goodwillie tower for simply connected, finite H-spaces converges.