On reconstructing Morse functions with prescribed level sets on $3$-dimensional manifolds and a necessary and sufficient condition for the reconstruction

Naoki Kitazawa

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arXiv · 2412.20626

On reconstructing Morse functions with prescribed level sets on $3$-dimensional manifolds and a necessary and sufficient condition for the reconstruction

Naoki Kitazawa

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Abstract

We discuss a necessary and sufficient condition for reconstruction of Morse functions with prescribed (regular) level sets on $3$-dimensional manifolds. The present work strengthens a previous result of the author where only sufficient conditions are studied. Our new work is also regarded as a kind of addenda.

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Naoki Kitazawa. 2024-12-30. On reconstructing Morse functions with prescribed level sets on $3$-dimensional manifolds and a necessary and sufficient condition for the reconstruction. https://arxiv.org/abs/2412.20626

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