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August 2018 Manifolds Which Admit Maps with Finitely Many Critical Points Into Spheres of Small Dimensions
Louis Funar, Cornel Pintea
Michigan Math. J. 67(3): 585-615 (August 2018). DOI: 10.1307/mmj/1529460326

Abstract

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.

Citation

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Louis Funar. Cornel Pintea. "Manifolds Which Admit Maps with Finitely Many Critical Points Into Spheres of Small Dimensions." Michigan Math. J. 67 (3) 585 - 615, August 2018. https://doi.org/10.1307/mmj/1529460326

Information

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

zbMATH: 06969985
MathSciNet: MR3835565
Digital Object Identifier: 10.1307/mmj/1529460326

Subjects:
Primary: 57R45, 57R70, 58K05

Rights: Copyright © 2018 The University of Michigan

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Vol.67 • No. 3 • August 2018
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