几乎平坦相对向量丛与几乎单值对应
Almost flat relative vector bundles and the almost monodromy correspondence
摘要：
本文在一对拓扑空间上引入了（稳定）相对丛的几乎平坦性概念，并研究了它的基本性质.首先，我们证明了拓扑的几乎平坦性与光滑意义的几乎平坦性是等价的.利用流形的可扩性，构造了几乎平坦的稳定相对丛。其次，我们证明了几乎单值对应，即基本群的几乎平坦（稳定）相对丛与（稳定）相对拟表示之间的对应。
英文摘要：
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 by using the enlargeability of 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.
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