First Betti numbers of orbits of Morse functions on surfaces

Autor:	Kuznietsova, Iryna, Soroka, Yuliia
Rok vydání:	2019
Předmět:	Mathematics - Group Theory Mathematics - Algebraic Topology Mathematics - Geometric Topology Mathematics - K-Theory and Homology 20E22 20F16 57T15
Druh dokumentu:	Working Paper
Popis:	In this article we study algebraic properties of the specific class of groups $\mathcal{G}$ generated by direct products and wreath products. Such class of groups appears in calculation of fundamental groups of orbits of Morse functions on compact manifolds. We prove that for any group $G\in\mathcal{G}$ the ranks of the center $Z(G)$ and the quotient by commutator subgroup $G/[G,G]$ coincide. Moreover, this rank is a first Betti number of the orbit of Morse function.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1908.03014 Zobrazit plný text záznamu View this record from Arxiv