Examples of smooth maps with finitely many critical points in dimensions $(4,3)$, $(8,5)$ and $(16,9)$

Louis Funar (1) , Cornel Pintea (2) , Ping Zhang (3)

1 IF - Institut Fourier
2 University of Cluj - University of Cluj
3 Eastern Mediterranean University - Eastern Mediterranean University

We consider manifolds $M^{2n}$ which admit smooth maps into a connected sum of $S^1\times S^n$ with only finitely many critical points, for $n\in\{2,4,8\}$, and compute the minimal number of critical points.

Mots clés: Critical point; isolated singularity; Montgomery-Samelson singular fibration; Hopf fibration; homotopy sphere

Domaines: Topologie géométrique [math.GT]

Louis Funar, Cornel Pintea, Ping Zhang. Examples of smooth maps with finitely many critical points in dimensions $(4,3)$, $(8,5)$ and $(16,9)$. 2008. ⟨hal-00260737v2⟩