Discrete dynamics and differentiable stacks

Autor:	Cabrera, Alejandro, del Hoyo, Matias, Pujals, Enrique
Rok vydání:	2018
Předmět:	Mathematics - Dynamical Systems Mathematics - Algebraic Topology Mathematics - Differential Geometry 22A22 37C15 57M12
Zdroj:	Revista Matem\'atica Iberoamericana (2020)
Druh dokumentu:	Working Paper
DOI:	10.4171/rmi/1194
Popis:	In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold encodes the dynamics up to conjugation and inversion. We also prove a generalization of this result for arbitrary discrete groups and non-simply connected manifolds, and relate it to the covering theory of stacks. As applications, we obtain a geometric version of Rieffel's theorem on irrational rotations of the circle, we compute the stack-theoretic fundamental group of hyperbolic toral automorphisms, and we revisit the classification of lens spaces. Comment: Revised version, 24 pages, a section about the characteristic class of a dynamics was added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1804.00220 Zobrazit plný text záznamu View this record from Arxiv