The first Betti numbers of orbits of Morse functions on surfaces

• Date: 2021
• Main Authors: Kuznietsova, I. V., Soroka, Yu. Yu., I. V., Yu. Yu., Кузнєцова, І. В., Сорока, Ю. Ю.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2383
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 515.1 Let $M$ be a connected compact orientable surface and let $P$ be the real line $\mathbb{R}$ or circle $S^1.$ The group $\mathcal{D}$ of diffeomorphisms on $M$ acts in the space of smooth mappings $C^{\infty} (M,P)$ by the rule $(f,h)\longmapsto f\circ h,$ where $h \in \mathcal{D},$ $f\in C...