非连通曲面上Morse函数的非奇异扩展

Pub Date : 2021-01-01 DOI:10.2206/KYUSHUJM.75.23

Kentaro Iwamoto

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引用次数: 0

摘要

本文研究了莫尔斯函数在闭合可定向曲面上的非奇异扩展。这种莫尔斯函数的非奇异扩展，是指在以给定曲面为边界的紧致可定向3流形上对无临界点的函数的扩展。1977年，Curley从组合学的角度刻画了关联标记Reeb图上非奇异边界芽的非奇异扩展的存在性。我们应用Curley的结果证明了在一个闭合可定向(可能不连通)曲面上的每一个Morse函数对连通的3流形具有非奇异扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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NON-SINGULAR EXTENSIONS OF MORSE FUNCTIONS ON DISCONNECTED SURFACES

In this paper, we study non-singular extensions of Morse functions on closed orientable surfaces. By a non-singular extension of such a Morse function, we mean an extension to a function without critical points on some compact orientable 3-manifold having as boundary the given surface. In 1977, Curley characterized the existence of non-singular extensions of non-singular boundary germs in terms of combinatorics on associated labeled Reeb graphs. We apply Curley’s result to show that every Morse function on a closed orientable (possibly disconnected) surface has a non-singular extension to a 3-manifold that is connected.

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