Certain 3-manifolds are characterized by Morse functions with regular levels consisting only of spheres, tori, or Klein bottles.
Saeki, Reeb spaces of smooth functions on manifolds II , Res
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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.