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

Part of: Lie groups

Published online by Cambridge University Press:  13 May 2025

MICHAEL ZSHORNACK
MICHAEL ZSHORNACK*
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, U.S.A. e-mail: zshornack@northwestern.edu
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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 generalises a method due to Long and Thistlethwaite who used it to show that thin surface groups in $\textrm{SL}(2k+1,\mathbf{Z})$ exist for all k.

MSC classification

Secondary: 22E40: Discrete subgroups of Lie groups
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 179 , Issue 1 , July 2025 , pp. 63 - 78
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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