Department of Mathematics

Geometry and Topology

  •  Reza Bidar, MSU
  •  Connection blocking in SL(n,R) quotients.
  •  12/07/2017
  •  2:00 PM - 3:00 PM
  •  C304 Wells Hall

Let G be a connected Lie group and Γ⊂G a lattice. Connection curves of the homogeneous space M=G/Γ are the orbits of one parameter subgroups of G. To \textit{block} a pair of points m1,m2∈M is to find a \textit{finite} set B⊂M∖{m1,m2} such that every connecting curve joining m1 and m2 intersects B. The homogeneous space M is \textit{blockable} if every pair of points in M can be blocked. \par In this paper we investigate blocking properties of Mn=SL(n,R)/Γ, where Γ=SL(n,Z) is the integer lattice. We focus on M2 and show that the set of bloackable pairs is a dense subset of M2×M2, and we conclude manifolds Mn are not blockable. Finally, we review a quaternionic structure of SL(2,R) and a way for making co-compact lattices in this context. We show that the obtained quotient homogeneous spaces are not finitely blockable.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science