Integral Zariski dense surface groups in $\operatorname{SL}(n,\mathbf{R})$

Abstract

Given a number field $K$, we show that certain $K$-integral representations of closed surface groups can be deformed to being Zariski dense while preserving many useful properties of the original representation. This generalizes a method due to Long and Thistlethwaite who used it to show that thin surface groups in $\operatorname{SL}(2k+1,\mathbf{Z})$ exist for all $k$.