与单纯形结构和逆像相容的光滑映射
Smooth maps compatible with simplicial structures and inverse images
摘要：
作为Morse函数理论的一个高维版本，人们利用一般光滑映射对光滑流形进行了各种研究。作为基本结果，在这些研究中，他们发现这种映射的逆像常常限制源流形的类型。例如，如果一个一般映射使得一个正则值的逆像不是零协边的，那么它的{ \it Reeb}空间的同调群是非平凡的，该空间被定义为该映射的逆像的所有连通分量的空间，并且是一般光滑映射理论中的基本工具。在本文中，我们在新的适当的情况下，类似的结果。这些作品被认为是平冢和佐伯2013--4年作品的延伸。
英文摘要：
As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps often restrict the types of the source manifolds. For example, if a generic map such that the inverse image of a regular value is not null-cobordant, then the homology group of its {\it Reeb} space, which is defined as the space of all the connected components of inverse images of the map and a fundamental tool in the theory of generic smooth maps, is known to be non-trivial. In this paper, we show similar results in new appropriate situations. These works are regarded as extensions of works by Hiratuka and Saeki in 2013--4.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
