Особые точки морсовской формы и слоения

Author: Ирина Анатольевна Мельникова

Вестник МГУ (Сер. матем., мех.), vol. 4, pp. 37-40, 1996.

Abstract: Let $M$ be a smooth compact connected orientable $n$-dimensional manifold on which a 1-form $\omega$ with Morse singularities is defined. On the manifold $M$, a foliation with singularities $F_\omega$ is defined. The irrationality degree of the form $\omega$ is determined by $dirr \omega = rk_\mathbb{Q}\left\{\int_{z_1}\omega, ..., \int_{z_m}\omega\right\} − 1$, where $z_1, ..., z_m$ is the basis in $H_1(M)$. It is proved that in the case of a compact foliation, the irrationality degree of the form and the number of homologically independent leaves are determined by the difference of the numbers of singularities of index 0 and 1. (The paper provides no abstract; this abstract is adapted from a Zentralblatt review, with some correction of translation and terminology.)

Keywords: Morse forms; foliation; singularities (The paper provides no keywords; these keywords are adapted from a Zentralblatt review.)

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