Abstract
This paper is devoted to the estimates for the middle dimension homologies of codimension 2 submanifoldA of a smooth manifold X. Proofs are based on the information about homologies of the ramified covering of X branched alongA. This information is extracted from the Atiyah-Singer signature formulas and from some corollaries of the Smith theory.
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Literature cited
V. S. Itenberg, “The middle dimension homologies of a codimension 2 submanifold,” Funkts. Anal. Prilozhen.,8, No. 2, 39–44 (1974).
O. Ya. Viro, “Ramified coverings of manifolds with an edge,” Dissertation, Leningrad (1974).
V. A. Rokhlin, “Two-dimensional submanifolds of four-dimensional manifolds,” Funkts. Anal. Prilozhen.,5, No. 1, 48–60 (1971).
E. Thomas and J. Wood, “On manifolds representing homology classes in codimension 2,” Invent. Math.,24, No. 1, 63–89 (1974).
M. Kato and Y. Matsumoto, “Simply connected surgery of submanifolds in codimension two,” J. Math. Soc. Jpn.,24, No. 4, 586–608 (1972).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 56, pp. 182–185, 1976.
The author takes this oppotunity to express his gratitude to V. A. Rokhlin for the formulation of the problem and for his interest in this paper.
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Itenberg, V.S. Middle dimension homologies of a codimension 2 submanifold. II. J Math Sci 14, 1165–1168 (1980). https://doi.org/10.1007/BF01562059
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DOI: https://doi.org/10.1007/BF01562059