长结空间的Goodwillie协单纯形模型及其应用

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2023-08-02 DOI:10.1007/s40062-023-00327-0

Yuqing Shi

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引用次数: 1

摘要

我们给出了Goodwillie观察到的从区间的一类开子集到紧生成的弱Hausdorff空间的类的共简单空间和好函子之间的对应关系的细节。使用它，我们计算纤维塔的积分Bousfield–Kan同伦谱序列的第一页，该序列由与长结空间相关的嵌入函子的Taylor塔给出。基于Conant中的方法（Am J Math 130（2）：341–357。https://doi.org/10.1353/ajm.2008.0020，2008），我们通过引入（i，n）标记的单位竞争图的概念，给出了对角项的微分映射的组合解释。

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Goodwillie’s cosimplicial model for the space of long knots and its applications

We work out the details of a correspondence observed by Goodwillie between cosimplicial spaces and good functors from a category of open subsets of the interval to the category of compactly generated weak Hausdorff spaces. Using this, we compute the first page of the integral Bousfield–Kan homotopy spectral sequence of the tower of fibrations, given by the Taylor tower of the embedding functor associated to the space of long knots. Based on the methods in Conant (Am J Math 130(2):341–357. https://doi.org/10.1353/ajm.2008.0020, 2008), we give a combinatorial interpretation of the differentials \(d^1\) mapping into the diagonal terms, by introducing the notion of (i, n)-marked unitrivalent graphs.

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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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