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Maps with finitely many critical points into high dimensional manifolds
Revista Matemática Complutense ( IF 0.8 ) Pub Date : 2020-06-18 , DOI: 10.1007/s13163-020-00362-y
Louis Funar

Assume that there exists a smooth map between two closed manifolds \(M^m\rightarrow N^k\), where \(2\le k\le m\le 2k-1\), with only finitely many singular points, all of which are cone-like. If \((m,k)\not \in \{(2,2), (4,3), (5,3), (8,5), (16,9)\}\), then \(M^m\) admits a locally trivial topological fibration over \(N^k\) and there exists a smooth map \(M^m\rightarrow N^k\) with at most one critical point.



中文翻译:

映射具有有限多个临界点的高维流形

假设两个闭合流形\(M ^ m \ rightarrow N ^ k \)之间存在一个平滑映射,其中\(2 \ le k \ le m \ le 2k-1 \)仅具有有限的奇异点,所有其中是锥形的。如果\((M,K)\不\在\ {(2,2),(4,3),(5,3),(8,5),(16,9)\} \) ,然后\ (M ^ m \)允许在\(N ^ k \)上进行局部琐碎的拓扑纤维化,并且存在具有至多一个临界点的平滑图\(M ^ m \ rightarrow N ^ k \)

更新日期:2020-06-18
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