论文标题
减少悬浮液的基本组在本地不含
Fundamental groups of reduced suspensions are locally free
论文作者
论文摘要
在本文中，我们分析了简化的悬架$σx$的基本组$π_1（σx，\ overline {x_0}）$，其中$（x，x_0）$是基于任意的Hausdorff Space。我们表明$π_1（σx，\ edlline {x_0}）$在典型上是同态至直接限制$ \ varinjlim_ {a \ in \ mathscr {p}}π_1（σa，= a，\ edimelline {x_0} $ sprodline $ fline $π_1（et）{有限生成的自由组或无限耳环组的同构。这种表征的直接后果是$π_1（σx，\ edimine {x_0}）$对于任何Hausdorff Space $ x $都是本地免费的。此外，我们表明，$σx$仅在且仅当$ x $依次连接到$ x_0 $时，仅当$ x $连接。
In this paper, we analyze the fundamental group $π_1(ΣX,\overline{x_0})$ of the reduced suspension $ΣX$ where $(X,x_0)$ is an arbitrary based Hausdorff space. We show that $π_1(ΣX,\overline{x_0})$ is canonically isomorphic to a direct limit $\varinjlim_{A\in\mathscr{P}}π_1(ΣA,\overline{x_0})$ where each group $π_1(ΣA,\overline{x_0})$ is isomorphic to a finitely generated free group or the infinite earring group. A direct consequence of this characterization is that $π_1(ΣX,\overline{x_0})$ is locally free for any Hausdorff space $X$. Additionally, we show that $ΣX$ is simply connected if and only if $X$ is sequentially $0$-connected at $x_0$.
