Topological Hochschild homology of X(n)

2017/08/30 by Jonathan Beardsley, Beardsley, Jonathan
Mathematics · #55P42 #55P43 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1708.09486

openalex publication_date 2017/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Ravenel's spectrum X(2) is the versal E₁-S-algebra of characteristic η. This implies that every E₁-S-algebra R of characteristic η admits an E₁-ring map X(2)→ R, i.e. an \mathbbA_∞ complex orientation of degree 2. This implies that R^∗(ℂP²)≅ R_∗[x]/x³. Additionally, if R is an 𝔼₂-ring Thom spectrum admitting a map (of homotopy ring spectra) from X(2), e.g. X(n), its topological Hochschild homology has a simple description.

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