不稳定全局同伦理论中的算子

IF 0.6 3区数学 Q3 MATHEMATICS Algebraic and Geometric Topology Pub Date : 2023-09-26 DOI:10.2140/agt.2023.23.3293

Miguel Barrero

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引用次数: 3

摘要

本文研究了不稳定整体同伦理论中的算子，即具有所有紧李群相容作用的空间的同伦理论。我们证明了这些操作数的理论非常有效，例如，可以给出任何此类操作数上代数范畴的模型结构。我们定义了全局的$E_\infty$ -操作数，将$E_\infty$ -操作数很好地推广到全局设置，并给出了代数在它们上面的校正结果。

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Operads in unstable global homotopy theory

In this paper we study operads in unstable global homotopy theory, which is the homotopy theory of spaces with compatible actions by all compact Lie groups. We show that the theory of these operads works remarkably well, as for example it is possible to give a model structure for the category of algebras over any such operad. We define global $E_\infty$-operads, a good generalization of $E_\infty$-operads to the global setting, and we give a rectification result for algebras over them.

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