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

2024/12/30 by Naoki Kitazawa, Kitazawa, Naoki
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2412.20626

openalex publication_date 2024/12/30 · openalex created_date 2025/01/01 · openalex updated_date 2026/07/29

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.

Related

• On reconstructing Morse-Bott functions with prescribed preimages on 3-dimensional manifolds and conditions for the reconstruction
• On a classification of Morse functions on 3-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one
• Characterizing 3-dimensional manifolds represented as connected sums of Lens spaces, S² × S¹, and torus bundles over the circle by certain Morse-Bott functions
• Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages
• Construction of real algebraic functions with prescribed preimages