Department of Mathematics

Geometry and Topology

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

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.



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