2010/11/12 by Thomas Koberda, Koberda, Thomas
Mathematics · #20F67 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT #msc:20F67
paper · pdf · doi:10.48550/arxiv.1011.2811
Some minor changes. Accepted to New York J. Math
openalex publication_date 2010/11/12 · arxiv created 2011/12/05 · arxiv updated 2011/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study the space of left- and bi-invariant orderings on a torsion-free nilpotent group G. We will show that generally the set of such orderings is equipped with a faithful action of the automorphism group of G. We prove a result which allows us to establish the same conclusion when G is assumed to be merely residually torsion-free nilpotent. In particular, we obtain faithful actions of mapping class groups of surfaces. We will draw connections between the structure of orderings on residually torsion-free nilpotent, hyperbolic groups and their Gromov boundaries, and we show that in those cases a faithful \Aut(G)-action on the boundary is equivalent to a faithful \Aut(G) action on the space of left--invariant orderings.