We introduce the abstract notion of a necklical set in order to describe a functorial combinatorial model of the path fibration over the geometric realization of a path connected simplicial set. In particular, to any path connected simplicial set X we associate a necklical set \({\widehat{{\varvec{\Omega }}}}X\) such that its geometric realization \(|{\widehat{{\varvec{\Omega }}}}X|\), a space built out of gluing cubical cells, is homotopy equivalent to the based loop space on |X| and the differential graded module of chains \(C_*({\widehat{{\varvec{\Omega }}}}X)\) is a differential graded associative algebra generalizing Adams’ cobar construction.

中文翻译：

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路径振动的组合模型

我们介绍了颈缩集合的抽象概念，以便描述在路径连接的单纯集合的几何实现上路径纤维化的函数组合模型。特别是，将与颈缩集合\（{\ widehat {{\ varvec {\ Omega}}}} X \关联的任何路径与简单集合X关联，以使其几何实现\（| {\ widehat {{\ varvec { \ Omega}}}} X | \），由粘合立方单元格构成的空间，同态等效于| X | 而链\（C _ *（{\ widehat {{\ varvec {\ Omega}}}}} X）\）的微分渐变模块是推广Adams的cobar构造的微分渐变关联代数。