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On the homology of a ramified covering over \(\mathbb{C}^2\). (English. Russian original) Zbl 0959.32031
Math. Notes 64, No. 6, 726-731 (1998); translation from Mat. Zametki 64, No. 6, 839-846 (1998).
Summary: The paper contains a description of the two-dimensional homology group of a specific surface, which is of interest in connection with the Jacobian conjecture. The self-intersection index and the value of the Chern characteristic of a generator of this group are calculated explicitly.

MSC:
32H99 Holomorphic mappings and correspondences
14R15 Jacobian problem
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[1] A. G. Vitushkin, ”Some examples related to the problem of polynomial transformations of \(\mathbb{C}\) n ,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],35, 269–279 (1971). · Zbl 0216.35801
[2] P. B. Kronheimer and T. Mrowka, ”The genus of embedded surfaces in the projective plane,”Math. Res. Lett.,1, 797–808 (1994). · Zbl 0851.57023
[3] J. W. Morgan, Z. Szabo, and C. H. Taubes, ”A product formula for Seiberg-Witten invariants and the generalized Thom conjecture,”J. Differential Geom.,44, 706–788 (1996). · Zbl 0974.53063
[4] S. Yu. Nemirovskii, ”Holomorphic functions and embedded real surfaces,”Mat. Zametki [Math. Notes],63, No. 4, 599–606 (1998).
[5] S. Yu. Nemirovskii, ”On embeddings of the two-sphere in Stein surfaces,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],362, No. 4 (1998).
[6] S. Yu. Orevkov, ”Three-sheeted polynomial mappings of \(\mathbb{C}\)2,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],50, 1231–1241 (1986). · Zbl 0624.13016
[7] A. V. Domrina and S. Yu. Orevkov, ”Four-sheeted polynomial mappings of \(\mathbb{C}\)2. I. The case of an irreducible ramification curve,”Mat. Zametki [Math. Notes],64, No. 6, 847–862 (1998). · Zbl 0955.14044
[8] S. Yu. Orevkov, ”Rudolph diagrams and an analytic realization of the Vitushkin covering,”Mat. Zametki [Math. Notes],60, No. 2, 206–224 (1996). · Zbl 0897.57002
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