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Maximal isotropic subspaces of skew-symmetric bilinear mapping. (English. Russian original) Zbl 0957.57018
Mosc. Univ. Math. Bull. 54, No. 4, 1-3 (1999); translation from Vestn. Mosk. Univ., Ser I 1999, No. 4, 3-5 (1999).
The paper continues the author’s investigations [I. A. Mel’nikova, Math. Notes 58, No. 6, 1302-1305 (1995); translation from Mat. Zametki 58, No. 6, 872-877 (1995; Zbl 0857.57030); Russ. Math. Surv. 50, No. 2, 444-445 (1995); translation from Usp. Mat. Nauk 50, No. 3, 217-218 (1995; Zbl 0859.58005)] in which the compactness problem for the Morse form foliation on a closed manifold $$M^n$$ is considered. The author discusses the problem of calculation of the maximal isotropic subgroup in $$H_{n-1}(M)$$ with respect to the operation of intersection of homology classes. The upper and lower estimates are established and some examples are considered when $$M=T^n$$ is an $$n$$-dimensional torus and $$M=M^2_g$$.

##### MSC:
 57R30 Foliations in differential topology; geometric theory 57M07 Topological methods in group theory 54H10 Topological representations of algebraic systems