Characterizing certain classes of $6$-dimensional closed and simply-connected manifolds via special generic maps
Naoki Kitazawa
备注：
21 pages, Main Theorem 4 added, additional expositions added to some proofs, this is submitted to a refereed journal. arXiv admin note: text overlap with arXiv:2202.00883
The present paper finds new necessary and sufficient conditions for $6$-dimensional closed and simply-connected manifolds of certain classes to admit special generic maps into certain Euclidean spaces.
The class of special generic maps naturally contains Morse functions with exactly two singular points on spheres in so-called Reeb's theorem, characterizing spheres topologically, and canonical projections of unit spheres. Our paper concerns variants of Reeb's theorem. Several results are known e. g. the cases where the manifolds of the targets are the plane and some cases where the manifolds of the domains are closed and simply-connected. Our paper concerns $6$-dimensional versions of a result of Nishioka, determining $5$-dimensional closed and simply-connected manifolds admitting special generic maps into Euclidean spaces completely. Closed and simply-connected manifolds are central geometric objects in (classical) algebraic topology and differential topology. The $6$-dimensional case is more complicated than the $5$-dimensional one: they are classified via explicit algebraic systems.
Diffeomorphism types of simply connected $3$-dimensional Mori fibre spaces
School of Mathematics, Shandong University（山东大学数学学院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院；中国科学院大学）；University of Chinese Academy of Sciences（广西民族大学数学科学学院）；School of Mathematical Sciences, Guangxi Minzu University
Rational homotopy and simply-connected 8-manifolds
引入了拓扑空间的有理同伦不变量P，它是上同调的五次张量。当n > 1时，维数不超过5 n-2的闭（n-1）-连通流形的形式等价于P和克劳利和第二作者arXiv：1505.04184引入的Bianchi-Massey张量的消失。我们还证明了闭单连通自旋8-流形群的上同调为S ^2 x S ^6的r重连通和的元素在挠率之前由P的值确定。
