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Slapar, Marko (2011)
Languages: English
Types: Preprint
Subjects: 32V40, 32S20, 32F10, Mathematics - Complex Variables

Classified by OpenAIRE into

arxiv: Mathematics::Symplectic Geometry, Mathematics::Geometric Topology, Mathematics::Differential Geometry
In this paper we examine the structure of complex points of real 4-manifolds embedded into complex 3-manifolds up to isotopy. We show that there are only two types of complex points up to isotopy and as a consequence, show that any such embedding can be deformed by isotopy to a manifold having 2-complete neighborhood basis.
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    • 1. Bishop, E., Differentiable manifolds in complex Euclidean space. Duke Math. J. 32 (1965), 1-21.
    • 2. Burcea, V., A normal form for a real 2-codimensional submanifold in CN+1 near a CR singularity. Preprint.
    • 3. Y. Eliashberg and V.M. Harlamov, On the number of complex points of a real surface in a complex surface, Proc. Leningrad int. Topology Conf. (1982),143-148
    • 4. Chirka, E. M., An introduction to the geometry of CR manifolds. Uspekhi Mat. Nauk 46 (1991), no. 1(277), 81-164, 240; translation in Russian Math. Surveys 46 (1991), no. 1, 95197
    • 5. Coffman, A., CR singularities of real fourfolds in C3, Illinois Journal of Mathematics, (3) 53 (2009), 939-981.
    • 6. ---- CR singular immersions of complex projective spaces. Beitrge Algebra Geom. 43 (2002), no. 2, 451477.
    • 7. Dolbeault, P., Tomassini, G., Zaitsev, D., On boundaries of Levi-flat hypersurfaces in Cn. C. R. Math. Acad. Sci. Paris 341 (2005), no. 6, 343-348.
    • 8. ---- , On Levi-flat hypersurfaces with prescribed boundary. Pure Appl. Math. Q. 6 (2010), no. 3, Special Issue: In honor of Joseph J. Kohn. Part 1, 725-753.
    • 9. Fintushel, R., Stern, R., Immersed spheres in 4-manifolds and the immersed Thom conjecture. Turkish J. Math. 19(2) (1995) 145-157.
    • 10. Forstneriˇc, F., Complex tangents of real surfaces in complex surfaces. Duke Math. J. 67 (1992), no. 2, 353-376.
    • 11. Horn, R. A.; Sergeichuk, V. V., Canonical forms for complex matrix congruence and *congruence. Linear Algebra Appl., 416 (2006), no. 2-3, 1010-1032.
    • 12. Huang, X.; Yin, W., A codimension two CR singular submanifold that is formally equivalent to a symmetric quadric. Int. Math. Res. Not. 15 (2009), 2789-2828.
    • 13. Lai, H. F., Characteristic classes of real manifolds immersed in complex manifolds, Trans. AMS 172 (1972), 1-33.
    • 14. Lisca P., Matic G., Tight contact structures and Seiberg-Witten invariants. Invent. Math. 128 (1997), 509-525.
    • 15. Moser, J. K., Webster, S. M., Normal forms for real surfaces in C2 near complex tangents and hyperbolic surface transformations. Acta Math. 150 (1983), no. 3-4, 255- 296.
    • 16. Nemirovski, S., Complex analysis and differential topology on complex surfaces. Uspekhi Math. Nauk 45(4) (1999), 47-74.
    • 17. Ozsv´ath P., Szab´o Z., The symplectic Thom conjecture. Ann. Math. (2) 151 (2000), 93-124.
    • 18. Slapar, M., On Stein neighborhood basis of real surfaces. Math. Z. 247 (2004), no. 4, 863-879.
    • 19. Thom, R., Un lemme sur les applications diffrentiables. Bol. Soc. Mat. Mexicana (2) 1 1956, 59-71. University of Ljubljana, Faculty of Education, Kardeljeva Ploˇscˇad 16, 1000 Ljubljana, Slovenia E-mail address:
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