论文标题
拓扑单型的无限通勤和基本群体
Infinitary commutativity and fundamental groups of topological monoids
论文作者
论文摘要
著名的埃克曼·希尔顿（Eckmann-Hilton）原则可以应用于证明$ h $ - 空间的基本群体是可交换的。在本文中，我们确定了Eckmann-Hilton原理的无限类似物，该类似于所有拓扑单型单体的基本组和称为$δ$ monoids的基本组。特别是，我们表明，每个$δ$ -MONOID $ M $都是“转让$π_1$ - 交互”的意义，因为任何无限的环路征收因子的因素被置于无数次无限订单所索引的因素，并且基于M $ e \ in M $ e \ in M $是同质的无效动作。我们还提供了詹姆斯还原产品的基本群体的详细说明，并应用了$π_1$ - 交换性来进行多个计算。
The well-known Eckmann-Hilton Principle may be applied to prove that fundamental groups of $H$-spaces are commutative. In this paper, we identify an infinitary analogue of the Eckmann-Hilton Principle that applies to fundamental groups of all topological monoids and slightly more general objects called pre-$Δ$-monoids. In particular, we show that every pre-$Δ$-monoid $M$ is "transfinitely $π_1$-commutative" in the sense that permutation of the factors of any infinite loop-concatenation indexed by a countably infinite order and based at the identity $e\in M$ is a homotopy invariant action. We also give a detailed account of fundamental groups of James reduced products and apply transfinite $π_1$-commutativity to make several computations.
