Computations of relative topological coHochschild homology

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2022-08-05 DOI:10.1007/s40062-022-00312-z

Sarah Klanderman

引用次数: 3

Abstract

Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, and Bohmann–Gerhardt–Høgenhaven–Shipley–Ziegenhagen developed a coBökstedt spectral sequence to compute the homology of \(\mathrm {coTHH}\) for coalgebras over the sphere spectrum. We construct a relative coBökstedt spectral sequence to study \(\mathrm {coTHH}\) of coalgebra spectra over any commutative ring spectrum R. Further, we use algebraic structures in this spectral sequence to complete some calculations of the homotopy groups of relative topological coHochschild homology.

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相对拓扑coHochschild同调的计算

Hess和Shipley定义了一个称为拓扑coHochschild同调的协代数谱不变量，Bohmann-Gerhardt-Høgenhaven-Shipley-Ziegenhagen开发了一个coBökstedt谱序列来计算球谱上的协代数\(\mathrm {coTHH}\)的同调性。构造了一个相对coBökstedt谱序列来研究任意交换环谱r上的协代数谱\(\mathrm {coTHH}\)，并利用该谱序列中的代数结构完成了相对拓扑coHochschild同调的同伦群的计算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.