Higher order Toda brackets

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2021-07-27 DOI:10.1007/s40062-021-00285-5

Aziz Kharoof

引用次数: 0

Abstract

We describe two ways to define higher order Toda brackets in a pointed simplicial model category \({\mathcal {D}}\): one is a recursive definition using model categorical constructions, and the second uses the associated simplicial enrichment. We show that these two definitions agree, by providing a third, diagrammatic, description of the Toda bracket, and explain how it serves as the obstruction to rectifying a certain homotopy-commutative diagram in \({\mathcal {D}}\).

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高阶Toda括号

我们描述了在点简单模型类别\({\mathcal {D}}\)中定义高阶Toda括号的两种方法:一种是使用模型分类结构的递归定义，另一种是使用相关的简单充实。我们通过提供Toda括号的第三个图解描述来证明这两个定义是一致的，并解释了它如何成为纠正\({\mathcal {D}}\)中某个同伦交换图的障碍。

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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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.

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