亚当斯的科巴结构是基于环空间的单项式-代数模型

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2024-05-15 DOI:10.1017/fms.2024.50

Anibal M. Medina-Mardones, Manuel Rivera

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引用次数: 0

摘要

我们证明，亚当斯关于尖空间奇异链的科巴构造与基于其循环空间的奇异立方链的经典映射是一个准同构，保留了明确定义的单环$E_\infty $ -代数结构。这一贡献将鲍斯的一个结果扩展到了最终结论，即亚当斯映射保留了单环代数结构。

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Adams’ cobar construction as a monoidal -coalgebra model of the based loop space

We prove that the classical map comparing Adams’ cobar construction on the singular chains of a pointed space and the singular cubical chains on its based loop space is a quasi-isomorphism preserving explicitly defined monoidal

$E_\infty $

-coalgebra structures. This contribution extends to its ultimate conclusion a result of Baues, stating that Adams’ map preserves monoidal coalgebra structures.

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来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.