Immersions of surfaces in almost–complex 4–manifolds

Bohr, Christian

doi:10.1090/S0002-9939-01-06185-8

Immersions of surfaces in almost–complex 4–manifolds
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Proc. Amer. Math. Soc. 130 (2002), 1523-1532 Request permission

Abstract:

In this paper, we investigate the relation between double points and complex points of immersed surfaces in almost–complex 4–manifolds and show how estimates for the minimal genus of embedded surfaces lead to inequalities between the number of double points and the number of complex points of an immersion.

References

W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574, DOI 10.1007/978-3-642-96754-2
Christian Bohr, Embedded surfaces and almost complex structures, Proc. Amer. Math. Soc. 128 (2000), no. 7, 2147–2154. MR 1657766, DOI 10.1090/S0002-9939-99-05277-6
C. Bohr, Embedded surfaces and the intersection forms of non–simply connected 4–manifolds, Ph.D. thesis, University of Munich (2000).
M. Chkhenkeli, T. Garrity, Intersection form and CR geometry for four–manifolds: the Kirby–Lai adjunction formula, Preprint, math.DG/9904007.
Ronald Fintushel and Ronald J. Stern, Immersed spheres in $4$-manifolds and the immersed Thom conjecture, Turkish J. Math. 19 (1995), no. 2, 145–157. MR 1349567
Patrick M. Gilmer, Configurations of surfaces in $4$-manifolds, Trans. Amer. Math. Soc. 264 (1981), no. 2, 353–380. MR 603768, DOI 10.1090/S0002-9947-1981-0603768-7
Michel A. Kervaire and John W. Milnor, On $2$-spheres in $4$-manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1651–1657. MR 133134, DOI 10.1073/pnas.47.10.1651
P. B. Kronheimer and T. S. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994), no. 6, 797–808. MR 1306022, DOI 10.4310/MRL.1994.v1.n6.a14
Hon Fei Lai, Characteristic classes of real manifolds immersed in complex manifolds, Trans. Amer. Math. Soc. 172 (1972), 1–33. MR 314066, DOI 10.1090/S0002-9947-1972-0314066-8
Terry Lawson, The minimal genus problem, Exposition. Math. 15 (1997), no. 5, 385–431. MR 1486407
T. J. Li and A. Liu, Symplectic structure on ruled surfaces and a generalized adjunction formula, Math. Res. Lett. 2 (1995), no. 4, 453–471. MR 1355707, DOI 10.4310/MRL.1995.v2.n4.a6
V.A. Rokhlin, Two–dimensional submanifolds of four–dimensional manifolds, Funct. Anal. Appl. 5 (1971), p. 39–48.