论文标题
承认特殊通用地图及其不错的广义多幅的流形
Manifolds admitting special generic maps and their nice generalized multisections
论文作者
论文摘要
我们表明，承认特殊通用地图的多种多样也承认了不错的广义多剖面。 特殊的通用图是摩尔斯功能的自然通用版本，在封闭的歧管上恰好有两个奇异点，表征了球体的尺寸不是$ 4 $拓扑的$ 4 $，而$ 4 $维的单位球体以及单位球体的规范投影。它们被证明可以限制球体等的可区分结构，而Saeki，Sakuma等则强烈地具有更一般的流形的拓扑结构，其次是Nishioka，Wrazidlo等，然后是作者。一些基本或重要的歧管也承认了这样的地图。 （概括）多种歧管的多凹是（紧凑）歧管的不错的分解，概括了所谓的Heegaard分裂，为$ 3 $二维流形。 PL歧管已被证明具有鲁宾斯坦和蒂尔曼的某些特性的多个（广义）。
We show that manifolds admitting special generic maps also admit nice generalized multisections. Special generic maps are natural generalized versions of Morse functions with exactly two singular points on closed manifolds, characterizing spheres whose dimensions are not $4$ topologically and the $4$-dimensional unit sphere, and canonical projections of unit spheres. They are shown to restrict the differentiable structures of spheres etc. and topologies of more general manifolds strongly by Saeki, Sakuma etc., followed by Nishioka, Wrazidlo etc. and followed by the author. Some elementary or important manifolds also admit such maps. (Generalized) multisections of manifolds are nice decompositions of (compact) manifolds, generalizing so-called Heegaard splittings of $3$-dimensional manifolds. PL manifolds have been shown to have (generalized) multisections enjoying certain properties by Rubinstein and Tillmann.
