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math.GT2022
On smooth functions with two critical values
Antonio Lerario, Chiara Meroni, Daniele Zuddas
We prove that every smooth closed manifold admits a smooth real-valued function with only two critical values. We call a function of this type a \emph{Reeb function}. We prove that…
math.GT2022
On Stiefel's parallelizability of 3-manifolds
Valentina Bais, Daniele Zuddas
We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting.