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Topological classification of 4-dimensional complete intersections. (English) Zbl 0866.57015
The main result of the paper is: Two 4-dimensional complete intersections of a complex projective space are homeomorphic if and only if they have the same total degree, Pontryagin numbers and Euler number.
For dimension 1 and 3 the diffeomorphism classification is well known by surface theory and the classification of 1-connected 6-manifolds [A. V. Zhubr, Math. USSR, Izv. 9(1975), 793-812 (1976); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 39, 839-859 (1975; Zbl 0318.57019)], for dimension 2 the topological classification is known by M. Freedman’s results. For higher dimensions it is still open. In fact, the authors classify certain more general 1-connected 8-manifolds using bordism structure.
Remark: The numbers mentioned in the Theorem are computed from the total Chern class, not in the paper but presented there.

MSC:
57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
14M10 Complete intersections
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