论文标题
叶叶的同构群在叶子空间上的作用
Actions of groups of foliated homeomorphisms on spaces of leaves
论文作者
论文摘要
让$δ$成为拓扑歧管$ x $，$ y $作为叶子的空间，而$ p：x \ y $是自然投影。与$ p $相对于因子拓扑的eng $ y $。然后，$ x $ $ x $的同质形态$ x $ $ x $的$ \ nathcal {当$ψ$相对于相应的紧凑型开放拓扑连续时，我们会提供足够的条件。实际上，类似的结果不仅适用于叶子，还适用于更一般的分区$Δ$的本地紧凑型Hausdorff Spaces $ x $。
Let $Δ$ be a foliation on a topological manifold $X$, $Y$ be the space of leaves, and $p: X \to Y$ be the natural projection. Endow $Y$ with the factor topology with respect to $p$. Then the group $\mathcal{H}(X, Δ)$ of foliated (i.e. mapping leaves onto leaves) homeomorphisms of $X$ naturally acts on the space of leaves $Y$, which gives a homomorphism $ψ: \mathcal{H}(X, Δ) \to \mathcal{H}(Y)$. We present sufficient conditions when $ψ$ is continuous with respect to the corresponding compact open topologies. In fact similar results hold not only for foliations but for a more general class of partitions $Δ$ of locally compact Hausdorff spaces $X$.
