Invariants of nonflat manifolds (Q1916669)

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)].