报告题目：Transformation theorems for almost splitting maps and some applications

报告人：黄显涛（中山大学）

报告时间：2022/11/07 16:00-18:00 (GMT+08:00) 中国标准时间 - 北京

报告地点：腾讯会议：811-108-530 会议密码：1958 

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https://meeting.tencent.com/dm/PDVbtUWAtZ14

报告摘要：The almost splitting map is a powerful tool in studying manifolds with Ricci curvature uniformly bounded from below and their Gromov-Hausdorff limits. In this talk, we will introduce a new transformation theorem for almost splitting maps. Compared with the previous known transformation theorems, such as the ones obtained by Cheeger-Naber and Cheeger-Jiang-Naber respectively, the new transformation theorem does not require the non-collapsed assumption. We will also introduce some applications of the new transformation theorem, one of which is a new smooth fibration theorem. Recall that Fukaya and Yamaguchi respectively proved smooth fibration theorems under certain sectional curvature condition, and later on, many authors try to study smooth fibration type theorems in the Ricci curvature case. Recently, we introduce a new notion, called generalized Reifenberg condition, under which we prove a smooth fibration theorem for collapsed manifolds with Ricci curvature lower bound, which gives a unified proof of smooth fibration theorems in many previous works, including the classical ones by Fukaya and Yamaguchi respectively. The new transformation theorem is a key tool in its proof. Some other applications of the transformation theorem will also be introduced in this talk. This talk is based on my joint work with Hongzhi Huang.