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Invariants of nonflat manifolds. (English. Russian original) Zbl 0858.53015
Funct. Anal. Appl. 29, No. 3, 180-187 (1995); translation from Funkts. Anal. Prilozh. 29, No. 3, 41-50 (1995).
The author obtains the homology groups and Euler-Poincaré characteristic of the set of singular hyperplanes and spheres which are tangent to a connected smooth closed manifold in a Euclidean space. The results are interesting and they are in connection with the author’s papers [Russ. Acad. Sci., Dokl., Math. 46, No. 2, 392-396 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 326, No. 6, 948-952 (1992; Zbl 0834.53008)] and [Funct. Anal. Appl. 27, No. 3, 205-210 (1993); translation from Funkts. Anal. Prilozh. 27, No. 3, 67-75 (1993; Zbl 0813.57022)].

MSC:
53A55 Differential invariants (local theory), geometric objects
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References:
[1] V. D. Sedykh, ?Invariants of convex manifolds,? Dokl. Ross. Akad. Nauk,326, No. 6, 948-952 (1992).
[2] V. D. Sedykh, ?Invariants of strictly convex manifolds,? Funkts. Anal. Prilozhen.,27, No. 3, 67-75 (1993). · Zbl 0813.57022
[3] V. I. Arnol’d, V. A. Vasil’ev, V. V. Goryunov, and O. V. Lyashko, Singularities. II. Classification and applications. Contemporary Problems in Mathematics. Fundamental directions [in Russian], Vol. 39, Itogi Nauki i Tekhniki, VINITI, Moscow (1989).
[4] V. M. Zakalyukin, ?Singularities of convex hulls of smooth manifolds,? Funkts. Anal. Prilozhen.,11, No. 3, 76-77 (1977). · Zbl 0376.60013
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