Characterizing 3-dimensional manifolds represented as connected sums of Lens spaces, S² × S¹, and torus bundles over the circle by certain Morse-Bott functions

2024/12/16 by Naoki Kitazawa, Kitazawa, Naoki · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2412.11397

openalex publication_date 2024/12/16 · openalex created_date 2024/12/18 · openalex updated_date 2026/07/28

Abstract

We characterize 3-dimensional manifolds represented as connected sums of Lens spaces, copies of S² × S¹, and torus bundles over the circle by certain Morse-Bott functions. This adds to our previous result around 2024, classifying Morse functions whose preimages containing no singular points are disjoint unions of spheres and tori on 3-dimensional manifolds represented as connected sums of connected sums of Lens spaces and copies of S² × S¹: we have strengthened and explicitized Saeki's result, characterizing the manifolds via such functions, in 2006. We apply similar arguments. However we discuss in a self-contained way essentially.

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• Smooth functions which are Morse on preimages of values not being local extrema and constructing natural functions of the class on connected sums of manifolds admitting these functions

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