论文标题
在平坦的歧管捆绑包上以及海夫莱格分类空间的连通性
On flat manifold bundles and the connectivity of Haefliger's classifying spaces
论文作者
论文摘要
我们研究了由于叶状歧管束的背景下，由于Haefliger和Thurston引起的猜想。在这种情况下，Haefliger-Thurston的猜想预测，每一个$ m $ - 捆绑在一个歧管$ b $上，其中$ \ text {dim}（b）\ leq \ leq \ text {dim}（dim}（m）$都是flat $ m $ m $ bundle的cobordant。特别是，我们研究了低维歧管上的平面$ M $捆的bordism类，将有限的尺寸谎言组$ g $与$ \ text {diff} _0（g）$进行了比较，并将其本地化为平坦的M型捆绑包的自由度。
We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston's conjecture predicts that every $M$-bundle over a manifold $B$ where $\text{dim}(B)\leq \text{dim}(M)$ is cobordant to a flat $M$-bundle. In particular, we study the bordism class of flat $M$-bundles over low dimensional manifolds, comparing a finite dimensional Lie group $G$ with $\text{Diff}_0(G)$ and localizing the holonomy of flat M-bundles to be supported in a ball.
