Examples of smooth maps with finitely many critical points in dimensions , and
Authors:
Louis Funar, Cornel Pintea and Ping Zhang
Journal:
Proc. Amer. Math. Soc. 138 (2010), 355365
MSC (2000):
Primary 57R45, 55R55, 58K05, 57R60, 57R70
Published electronically:
September 3, 2009
MathSciNet review:
2550201
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We consider manifolds which admit smooth maps into a connected sum of with only finitely many critical points, for , and compute the minimal number of critical points.
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 P. L. Antonelli, Differentiable MontgomerySamelson fiberings with finite singular sets, Canad. J. Math. 21(1969), 14891495. MR 0261624 (41:6237)
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 A. Dimca, Singularities and topology of hypersurfaces, SpringerVerlag, BerlinNew York, 1992. MR 1194180 (94b:32058)
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 R. E. Gompf and A. I. Stipsicz, manifolds and Kirby calculus, Graduate Studies in Mathematics, 20, American Mathematical Society, Providence, RI, 1999. MR 1707327 (2000h:57038)
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 A. Haefliger, Differentiable embeddings of in for , Ann. of Math. (2) 83(1966), 402436. MR 0202151 (34:2024)
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 W. Huebsch and M. Morse, Schoenflies extensions without interior differential singularities, Ann. of Math. (2) 76(1962), 1854. MR 0146847 (26:4366)
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Additional Information
Louis Funar
Affiliation:
Institut Fourier BP 74, UMR 5582, Université de Grenoble I, 38402 SaintMartind’Hères cedex, France
Email:
funar@fourier.ujfgrenoble.fr
Cornel Pintea
Affiliation:
Department of Geometry, “BabeşBolyai” University, 400084 M. Kogălniceanu 1, ClujNapoca, 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/S000299390910028X
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.
