论文标题
几乎分裂地图，转换定理和平滑纤维定理
Almost splitting maps, transformation theorems and smooth fibration theorems
论文作者
论文摘要
在本文中，我们介绍了一个称为广义的Reifenberg条件的概念，在该概念下，我们证明了在下面界定的RICCI曲率折叠的折叠式折叠定理，在下面有RICCI曲率，在许多先前的作品中提供了平滑纤维化定理的统一证明（包括福卡亚和Yamaguchi分别证明的作品）。该纤维化定理证明的一个关键工具是用于几乎分裂地图的转换技术，该技术源自Cheeger-naber（\ cite {cn}）和cheeger-jiang-naber（\ cite {cjn21}）。更准确地说，我们表明，Cheeger-Jiang-Naber的转换定理（请参阅\ cite {CJN21}）的命题7.7）可能会使可能崩溃的歧管（cjn21}}）。本文给出了转换定理的其他一些应用。
In this paper, we introduce a notion, called generalized Reifenberg condition, under which we prove a smooth fibration theorem for collapsed manifolds with Ricci curvature bounded below, which gives a unified proof of smooth fibration theorems in many previous works (including the ones proved by Fukaya and Yamaguchi respectively). A key tool in the proof of this fibration theorem is the transformation technique for almost splitting maps, which originates from Cheeger-Naber (\cite{CN}) and Cheeger-Jiang-Naber (\cite{CJN21}). More precisely, we show that a transformation theorem of Cheeger-Jiang-Naber (see Proposition 7.7 in \cite{CJN21}) holds for possibly collapsed manifolds. Some other applications of the transformation theorems are given in this paper.
