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

Michael Zshornack

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arXiv · 2211.08616

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

Michael Zshornack

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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 $k$.

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Michael Zshornack. 2022-11-16. Integral Zariski dense surface groups in $\operatorname{SL}(n,\mathbf{R})$. https://arxiv.org/abs/2211.08616

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