2025/11/04 by Chaminadour, Maxime
Computer Science · Mathematics · #55T05 (primary) 55N15 55P42 (secondary) #Algebraic Topology (math.AT) #Digital Image Processing Techniques #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2511.02346
openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
In this article, we extend the computation of topological Hochschild homology (THH) of the Adams summand ℓ of p-local connective complex topological K-theory (ku) to ku itself. We leverage the relation up-1 = v1, where u is a generator of ku_* and v1 is a generator of ℓ_*, and we consider the cofiber of the multiplication by v1 in ku, denoted ku/v1. We use the morphism between the Bockstein spectral sequences of the multiplication by v1 computing THH_*(ℓ) and THH_*(ku); we develop a general technique using what we term a gathered spectral sequence that allows us to explore the relationship between the Bockstein spectral sequences for the multiplications by v1 and u, from which we derive a complete computation of THH_*(ku). Our method is not only applicable to this specific problem but may also prove useful in other computations.