Topological aspects of the dynamical moduli space of rational maps

Autor:	Bergeron, Maxime, Filom, Khashayar, Nariman, Sam
Rok vydání:	2019
Předmět:	Mathematics - Algebraic Topology Mathematics - Dynamical Systems 14L30 37P45 55Q52 55R80 58D15
Zdroj:	Advances in Mathematics 397 (2022)
Druh dokumentu:	Working Paper
DOI:	10.1016/j.aim.2022.108209
Popis:	We investigate the topology of the space of M\"obius conjugacy classes of degree $d$ rational maps on the Riemann sphere. We show that it is rationally acyclic and we compute its fundamental group. As a byproduct, we also obtain the ranks of some higher homotopy groups of the parameter space of degree $d$ rational maps allowing us to extend the previously known range. Moreover, we show that this parameter space is not nilpotent. Comment: 35 pages. Minor corrections. To appear in Advances in Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1908.10792 Zobrazit plný text záznamu View this record from Arxiv