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CANCELLING COMPLEX POINTS IN CODIMENSION TWO

Part of: CR manifolds

Published online by Cambridge University Press:  09 August 2012

MARKO SLAPAR
MARKO SLAPAR*
Affiliation:
Faculty of Education, University of Ljubljana, Kardeljeva Ploščad 16, 1000 Ljubljana, Slovenia Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia (email: [email protected])
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Abstract

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A generically embedded real submanifold of codimension two in a complex manifold has isolated complex points that can be classified as either elliptic or hyperbolic. In this paper we show that a pair consisting of one elliptic and one hyperbolic complex point of the same sign can be cancelled by a $\mathcal {C}^{0}$small isotopy of embeddings.

Keywords

CR manifoldscomplex points

MSC classification

Secondary: 32V40: Real submanifolds in complex manifolds
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 1 , August 2013 , pp. 64 - 69
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

References

[1]Coffman, A., ‘CR singularities of real fourfolds in $C^3$’, Illinois J. Math. (3) 53 (2009), 939–981.Google Scholar
[2]Dolbeault, P., Tomassini, G. & Zaitsev, D., ‘On boundaries of Levi-flat hypersurfaces in $C^n$’, C. R. Math. Acad. Sci. Paris 341(6) (2005), 343–348.CrossRefGoogle Scholar
[3]Dolbeault, P., Tomassini, G. & Zaitsev, D., ‘On Levi-flat hypersurfaces with prescribed boundary’, Pure Appl. Math. Q. 6(3) (2010), 725–753, Special issue in honor of Joseph J. Kohn. Part 1.CrossRefGoogle Scholar
[4]Eliashberg, Y. & Harlamov, V. M., ‘On the number of complex points of a real surface in a complex surface’, Proc. Leningrad Int. Topol. Conf. (1982), 143–148.Google Scholar
[5]Eliashberg, Y. & Mishachev, N., Introduction to the h-principle, Graduate Studies in Mathematics, 48 (American Mathematical Society, Providence, RI, 2002).Google Scholar
[6]Forstnerič, F., ‘Complex tangents of real surfaces in complex surfaces’, Duke Math. J. 67(2) (1992), 353–376.CrossRefGoogle Scholar
[7]Forstnerič, F., Stein Manifolds and Holomorphic Mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 56 (Springer, Berlin, 2011).CrossRefGoogle Scholar
[8]Gromov, M., Partial Differential Relations, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 9 (Springer, Berlin, 1986).CrossRefGoogle Scholar
[9]Lai, H. F., ‘Characteristic classes of real manifolds immersed in complex manifolds’, Trans. Amer. Math. Soc. 172 (1972), 1–33.CrossRefGoogle Scholar
[10]Nemirovski, S., ‘Complex analysis and differential topology on complex surfaces’, Uspekhi Math. Nauk. 45(4) (1999), 47–74.Google Scholar
[11]Range, R. M. & Siu, Y. T., ‘$C^k$ approximation by holomorphic functions and $\bar \partial $ -closed forms on $C^k$ submanifolds of a complex manifold’, Math. Ann. 210 (1974), 105–122.CrossRefGoogle Scholar
[12]Slapar, M., ‘Modeling complex points up to isotopy’, J. Geom. Anal., to appear, doi:10.1007/s12220-012-9312-6.CrossRefGoogle Scholar