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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Louis Funar, Cornel Pintea and Ping Zhang
Journal: Proc. Amer. Math. Soc. 138 (2010), 355-365
MSC (2000): Primary 57R45, 55R55, 58K05, 57R60, 57R70
Published electronically: September 3, 2009
MathSciNet review: 2550201
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Abstract: 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.


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Additional Information

Louis Funar
Affiliation: Institut Fourier BP 74, UMR 5582, Université de Grenoble I, 38402 Saint-Martin-d’Hères cedex, France
Email: funar@fourier.ujf-grenoble.fr

Cornel Pintea
Affiliation: Department of Geometry, “Babeş-Bolyai” University, 400084 M. Kogălniceanu 1, Cluj-Napoca, Romania
Email: cpintea@math.ubbcluj.ro

Ping Zhang
Affiliation: Department of Mathematics, Eastern Mediterranean University, Gazimagusa, North Cyprus, via Mersin 10, Turkey
Email: ping.zhang@emu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10028-X
PII: S 0002-9939(09)10028-X
Keywords: Critical point, isolated singularity, Hopf fibration, suspension, homotopy sphere
Received by editor(s): July 21, 2008
Received by editor(s) in revised form: April 28, 2009
Published electronically: September 3, 2009
Communicated by: Paul Goerss
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.