E-infinity structure in hyperoctahedral homology
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Publication:6039219
DOI10.4310/HHA.2023.V25.N1.A1zbMATH Open1523.55008arXiv2108.05154MaRDI QIDQ6039219
Author name not available (Why is that?)
Publication date: 4 May 2023
Published in: (Search for Journal in Brave)
Abstract: Hyperoctahedral homology for involutive algebras is the homology theory associated to the hyperoctahedral crossed simplicial group. It is related to equivariant stable homotopy theory via the homology of equivariant infinite loop spaces. In this paper we show that there is an E-infinity algebra structure on the simplicial module that computes hyperoctahedral homology. We deduce that hyperoctahedral homology admits Dyer-Lashof homology operations. Furthermore, there is a Pontryagin product which gives hyperoctahedral homology the structure of an associative, graded-commutative algebra. We also give an explicit description of hyperoctahedral homology in degree zero. Combining this description and the Pontryagin product we show that hyperoctahedral homology fails to preserve Morita equivalence.
Full work available at URL: https://arxiv.org/abs/2108.05154
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