 

Dave Witte Morris and Kevin Wortman
Horospherical limit points of Sarithmetic groups view print


Published: 
April 10, 2012 
Keywords: 
Horospherical limit point, Sarithmetic group, Tits building, Ratner's theorem 
Subject: 
20G30 (Primary) 20E42, 22E40, 51E24 (Secondary) 


Abstract
Suppose Γ is an Sarithmetic subgroup of a connected, semisimple algebraic group G over a global field Q (of any characteristic). It is wellknown that Γ acts by isometries on a certain CAT(0) metric space X_{S} = ∏_{v ∈ S} X_{v}, where each X_{v} is either a Euclidean building or a Riemannian symmetric space. For a point ξ on the visual boundary of X_{S}, we show there exists a horoball based at ξ that is disjoint from some Γorbit in X_{S} if and only if ξ lies on the boundary of a certain type of flat in X_{S} that we call "Qgood.''
This generalizes a theorem of G.Avramidi and D.W.Morris that characterizes the horospherical limit points for the action of an arithmetic group on its associated symmetric space X.


Author information
Dave Witte Morris:
Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, T1K6R4, Canada
Dave.Morris@uleth.ca
Kevin Wortman:
Department of Mathematics, University of Utah, Salt Lake City, UT 841120090
wortman@math.utah.edu

