The Michigan Mathematical Journal

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

Louis Funar and Cornel Pintea

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We construct, for m6 and 2nm, closed manifolds Mm with finite nonzero φ(Mm,Sn), where φ(M,N) denotes the minimum number of critical points of a smooth map MN. We also give some explicit families of examples for even m6 and n=3, taking advantage of the Lie group structure on S3. Moreover, there are infinitely many such examples with φ(Mm,Sn)=1. Eventually, we compute the signature of the manifolds M2n occurring for even n.

Article information

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

Received: 17 November 2016
Revised: 24 July 2017
First available in Project Euclid: 20 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R45: Singularities of differentiable mappings 57R70: Critical points and critical submanifolds 58K05: Critical points of functions and mappings


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.

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