Incompressible solvable representations of surface groups
arXiv:1704.01007
Abstract
The fundamental group of every surface that is not the projective plane or Klein bottle has a representation to a torsion-free group of upper-triangular matrices in SL(2,R) with no simple loop (i.e. a nontrivial element representing a simple closed curve) in the kernel.
Minor revisions and corrections suggested by a referee. Accepted version