论文标题
拓扑中丰富的差分谎言代数
Enriched Differential Lie Algebras in Topology
论文作者
论文摘要
本文介绍了富含差异分级的LIE代数（EDGL）的新类别EDGL，与所有连接的CW复合物和简单集的拓扑直接相关。它具有类似于沙利文（Sullivan）用于交换差分级代数的同型理论。每个连接的空间都有一个独特的最小EDGL模型，并且代数过程将其连接到最小的沙利文模型。最小的EDGL模型自然代表联合振动，特别是细胞附件，EDGL和Sullivan模型之间的相互作用允许扩展到以前仅针对简单连接的空间建立的所有路径连接的结果。特别是，这提供了路径连接空间的经典sullivan合理化$ x \ to x _ {\ mathbb q} $的应用程序和有趣的示例。
This paper introduces a new category, Edgl, of enriched differential graded Lie algebras (edgl), directly related to the topology of all connected CW complexes and simplicial sets. It is equipped with a homotopy theory analogous to that developed by Sullivan for commutative differential graded algebras. Each connected space has a unique minimal edgl model, and an algebraic process connects this to the minimal Sullivan model. Minimal edgl models naturally represent cofibrations and, in particular cell attachments, and the interplay between edgl and Sullivan models permits the extension to all path connected spaces of results previously established only for simply connected spaces. This, in particular, provides applications and interesting examples of the classical Sullivan rationalization $X\to X_{\mathbb Q}$ of a path connected space.
