A Morse 2-function is a generic smooth map f from a manifold M of arbitrary finite dimension to a surface B . Its critical set maps to an immersed collection of cusped arcs in B . The aim of this paper is to explain exactly when it is possible to move these arcs around in B by a homotopy of f and to give a library of examples when M is a closed 4-manifold. The last two sections give applications to the theory of crown diagrams of smooth 4-manifolds.

中文翻译：

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存在二参数交叉，有应用

莫尔斯 2 函数是从任意有限维度的流形 M 到表面 B 的通用平滑映射 f。它的临界集映射到 B 中的尖弧的浸入集合。本文的目的是准确解释何时可以通过 f 的同伦在 B 中移动这些弧，并在 M 是封闭的 4 流形时给出一个示例库。最后两节给出了光滑 4 流形的冠状图理论的应用。