2016/11/03 by Amalie Høgenhaven, Høgenhaven, Amalie · 3 citations
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #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.1611.01204
openalex publication_date 2016/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute the G-equivariant homotopy type of the real topological cyclic homology of spherical group rings with anti-involution induced by taking inverses in the group, where G denotes the group Gal(ℂ/ℝ). The real topological Hochschild homology of a spherical group ring \mathbbS[Γ], with anti-involution as described, is an O(2)-cyclotomic spectrum and we construct a map commuting with the cyclotomic structures from the O(2)-equivariant suspension spectrum of the dihedral bar construction on Γ to the real topological Hochschild homology of \mathbbS[Γ], which induce isomorphisms on Cpn- and Dpn-homotopy groups for all n∈ ℤ and all primes p. Here Cpn is the cyclic group of order pn and Dpn is the dihedral group of order 2pn. Finally, we compute the G-equivariant homotopy type of the real topological cyclic homology of \mathbbS[Γ] at a prime p.