Topology of special generic maps of manifolds into Euclidean spaces
The author studies the global topology of special generic maps; i.e., smooth maps of closed \(n\)-manifolds into \(\mathbb{R}^ p\) \((p\leq n)\) all of whose singularities are the definite fold points. One of the main results is to determine completely those closed manifolds which admit special generic maps into \(\mathbb{R}^ 2\). This result is the final form. Partial results of it were given in [\textit{O. Burlet} and \textit{G. de Rham}, Enseign. Math., II. Sér. 20, 275-292 (1974; Zbl 0299.58005)] for \(n=3\) and [\textit{P. Porto jun.} and \textit{Y. K. S. Furuya}, Topology Appl. 35, No. 1, 41-52 (1990; Zbl 0715.57015)] for \(n>3\). This paper also contains many other results.
smooth maps of closed \(n\)-manifolds into \(\mathbb{R}^ p\)
special generic maps into \(\mathbb{R}^ 2\)
scientific article; zbMATH DE number 221869
scientific article