Singular fibers of stable maps and signatures of 4 – manifolds

Content Provider	Semantic Scholar
Author	Amamoto, Aeki T. Akahiro Y.
Copyright Year	2008
Abstract	In [24] the first named author developed the theory of singular fibers of generic differentiable maps between manifolds of negative codimension. Here, the codimension of a map f W M !N between manifolds is defined to be k D dim N dim M . For k 0, the fiber over a point in N is a discrete set of points, as long as the map is generic enough, and we can study the topology of such maps by using the well-developed theory of multi-jet spaces (see, for example, the article [13] by Mather). However, in the case where k < 0, the fiber over a point is no longer a discrete set, and is a complex of positive dimension k in general. This means that the theory of multi-jet spaces is not sufficient any more, and in [24] we have seen that the topology of singular fibers plays an essential role in such a study.
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Resource Type	Article