2021/06/29 by Sang-hyun Kim, Thomas Koberda, Kim, Sang-hyun +1 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.DS #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.2106.15532
291 pages, several figures
arxiv created 2021/06/29 · arxiv updated 2021/06/30
In this monograph, we give an account of the relationship between the algebraic structure of finitely generated and countable groups and the regularity with which they act on manifolds. We concentrate on the case of one--dimensional manifolds, culminating with a uniform construction of finitely generated groups acting with prescribed regularity on the compact interval and on the circle. We develop the theory of dynamical obstructions to smoothness, beginning with classical results of Denjoy, to more recent results of Kopell, and to modern results such as the abt--Lemma. We give a classification of the right-angled Artin groups that have finite critical regularity and discuss their exact critical regularities in many cases, and we compute the virtual critical regularity of most mapping class groups of orientable surfaces.