维数不超过8的复射影塔的分类与上同调刚性
几何拓扑
2015-12-03 v4 代数拓扑
摘要
复射影塔（简称-塔）是从一个点出发的迭代复射影纤维化。本文对所有6维-塔进行了微分同胚分类，并作为推论，证明了所有此类流形是上同调刚性的，即它们由上同调环完全决定到微分同胚。我们还通过对上的-纤维化进行微分同胚分类，证明了上同调刚性对8维-塔不成立。作为推论，我们证明如果此类-塔是同伦等价的，则它们是微分同胚的。
引用
@article{arxiv.1203.4403,
title = {Classification of complex projective towers up to dimension 8 and cohomological rigidity},
author = {Shintarô Kuroki and Dong Youp Suh},
journal= {arXiv preprint arXiv:1203.4403},
year = {2015}
}
备注
28 pages, v2: Remark 2.8 removed: This paper has been withdrawn by the author due to mistakes in Section 5, v3: corrected the results and proofs in Section 5