Vitushkin, A. G. 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. Cited in 1 Document MSC: 32H99 Holomorphic mappings and correspondences 14R15 Jacobian problem Keywords:ramified covering; Chern class; self-intersection index; homology group; Jacobian conjecture PDF BibTeX XML Cite \textit{A. G. Vitushkin}, Math. Notes 64, No. 6, 726--731 (1998; Zbl 0959.32031); translation from Mat. Zametki 64, No. 6, 839--846 (1998) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.