The Michigan Mathematical Journal

Manifolds Which Admit Maps with Finitely Many Critical Points Into Spheres of Small Dimensions

Abstract

We construct, for $m\geq6$ and $2n\leq m$, closed manifolds $M^{m}$ with finite nonzero $\varphi(M^{m},S^{n}$), where $\varphi(M,N)$ denotes the minimum number of critical points of a smooth map $M\to N$. We also give some explicit families of examples for even $m\geq6$ and $n=3$, taking advantage of the Lie group structure on $S^{3}$. Moreover, there are infinitely many such examples with $\varphi(M^{m},S^{n})=1$. Eventually, we compute the signature of the manifolds $M^{2n}$ occurring for even $n$.

Article information

Source
Michigan Math. J., Volume 67, Issue 3 (2018), 585-615.

Dates
Revised: 24 July 2017
First available in Project Euclid: 20 June 2018

https://projecteuclid.org/euclid.mmj/1529460326

Digital Object Identifier
doi:10.1307/mmj/1529460326

Mathematical Reviews number (MathSciNet)
MR3835565

Zentralblatt MATH identifier
06969985

Citation

Funar, Louis; Pintea, Cornel. Manifolds Which Admit Maps with Finitely Many Critical Points Into Spheres of Small Dimensions. Michigan Math. J. 67 (2018), no. 3, 585--615. doi:10.1307/mmj/1529460326. https://projecteuclid.org/euclid.mmj/1529460326

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