2023/11/12 by Logan Hyslop, Hyslop, Logan
Computer Science · Mathematics · #55R20 #55T25 (Primary) 19D55 (Secondary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2311.06717
openalex publication_date 2023/11/12 · openalex created_date 2023/11/15 · openalex updated_date 2026/07/28
We discuss spectral sequences coming from Whitehead filtrations in the computation of topological Hochschild homology of ring spectra. Using cyclic invariance, this makes for simple computations of THH of connective rings R with coefficients in discrete ring spectra. In particular, we show how to use this to compute THH(tmf,\mathbbF2), and THH(tmf,ℤ(2)), where tmf denotes the 𝔼_∞ ring spectrum of topological modular forms. Then, we obtain a description of THH(ℓ/v1n) in terms of THH(ℓ,ℓ/v1n), where the latter can be computed by results of arXiv:0710.4368. We next explain how the methods of this computation generalize to give us information about THH(cofib(xk:Σk|x|R→ R)) for R and cofib(xk) suitably structured connective ring spectra, k>1, and x∈ π*(R) an arbitrary element in positive degree. Finally, we examine the general framework to describe the topological Hochschild homology of 2-local connective self-conjugate K-theory, ksc2.