Certain 3-manifolds are characterized by Morse functions with regular levels consisting only of spheres, tori, or Klein bottles.
Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed mani- folds which may not be orientable , Methods of Functional Analysis and Topology Vol
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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.