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| Natura: | Preprint |
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2022
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| Accesso online: | https://arxiv.org/abs/2207.10029 |
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| _version_ | 1866910591603441664 |
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| author | Huang, Hongzhi Huang, Xian-Tao |
| author_facet | Huang, Hongzhi Huang, Xian-Tao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10029 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Almost splitting maps, transformation theorems and smooth fibration theorems Huang, Hongzhi Huang, Xian-Tao Differential Geometry 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. |
| title | Almost splitting maps, transformation theorems and smooth fibration theorems |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2207.10029 |