Maximal isotropic subspaces of skew-symmetric bilinear mapping. (English. Russian original) Zbl 0957.57018

Mel’nikova, I. A.

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 \(M=M^2_g\).

Reviewer: Vladislav A. Martynyuk (Kyïv)

MSC:

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

Keywords:

skew-symmetric bilinear mapping; isotropic subspace; Morse form

Citations:

Zbl 0857.57030; Zbl 0859.58005