Almost flat relative vector bundles and the almost monodromy correspondence
Almost flat relative vector bundles and the almost monodromy correspondence
复制标题
几乎平坦的相对向量丛和几乎单峰对应
DOI：
10.1142/s1793525320500545
复制
发表时间：
2020
影响因子：
0.8
通讯作者：
Kubota Yosuke
中科院分区：
文献类型：
--
作者：
Kubota Yosuke;Takeishi Takuya;Kubota Yosuke
本文引入了一对拓扑空间上（稳定）相对束的概平坦性概念，并研究了其基本性质。首先，我们证明了拓扑的几乎平坦度和光滑感是等价的。给出了可放大流形上的几乎平坦稳定相对束的构造。其次，我们证明了基本群的几乎单调对应，即基本群的几乎平坦（稳定）相对束与（稳定）相对拟表示之间的对应。
In this paper, we introduce the notion of almost flatness for (stably) relative bundles on a pair of topological spaces and investigate basic properties of it. First, we show that almost flatness of topological and smooth sense are equivalent. This provides a construction of an almost flat stably relative bundle on enlargeable manifolds. Second, we show the almost monodromy correspondence, that is, a correspondence between almost flat (stably) relative bundles and (stably) relative quasi-representations of the fundamental group.