流形允许某些显式特殊-类属映射的限制条件及利用流形构造映射
Restrictions on manifolds admitting certain explicit special-generic-like maps and construction of maps with the manifolds
摘要：
作者通过余维为负的光滑映射来观察和研究流形的代数拓扑或微分拓扑性质，从而引入了特殊类属映射或SGL映射.本文认为，流形承认某些非常明确的SGL映射是拓扑限制强，这也构造这些映射与流形明确。本文将球面或Reeb定理中的函数上具有两个奇点的Morse函数和自然嵌入球面在欧几里得空间中的正则投影推广为特殊的一般映射。它们良好的整体结构促使我们去研究这类映射和流形。流形表示为连通和的产品领域和类似的承认这样的地图在相当多的情况下。拓扑结构和微分结构的流形的域，这样的地图也强烈限制：由于佐伯和佐久间，其次是西冈，Wrazidlo和作者。考虑到它们的良好的全局结构，这些映射是广义的，这产生SGL映射。
英文摘要：
Special-generic-like maps or SGL maps are introduced by the author motivated by observing and investigating algebraic topological or differential topological properties of manifolds via nice smooth maps whose codimensions are negative. The present paper says that manifolds admitting certain very explicit SGL maps are topologically restricted strongly and this also constructs these maps with the manifolds explicitly. Morse functions with exactly two singular points on spheres or functions in Reeb's theorem and canonical projections of naturally embedded spheres in Euclidean spaces are generali5zed as special generic maps. Their nice global structures motivate us to study such maps and the manifolds. Manifolds represented as connected sums of the product of spheres and similar ones admit such maps in considerable cases. The topologies and the differentiable structures of the manifolds of the domains of such maps are also strongly restricted: due to Saeki and Sakuma, followed by Nishioka, Wrazidlo and the author. Respecting their nice global structures, these maps are generalized and this yields SGL maps.
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