Certain 3-manifolds are characterized by Morse functions with regular levels consisting only of spheres, tori, or Klein bottles.
Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396
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Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles
Certain 3-manifolds are characterized by Morse functions with regular levels consisting only of spheres, tori, or Klein bottles.