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<p>Let Δ be a cocompact lattice in Sp(<i>m</i>, 1), <i>m</i> ⩾ 2, or F<Stack> <sub>4</sub> <sup>(−20)</sup> </Stack>. We exhibit examples of finitely generated subgroups of Δ × Δ with positive first Betti number all of whose discrete faithful representations into any real semisimple Lie group are quasi-isometric embeddings. The examples of this paper are inspired by the counterexamples of Bass–Lubotzky [BL00] to Platonov’s conjecture.</p>

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Fiber products of rank 1 superrigid lattices and quasi-isometric embeddings

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Konstantinos Tsouvalas

摘要

Let Δ be a cocompact lattice in Sp(m, 1), m ⩾ 2, or F 4 (−20) . We exhibit examples of finitely generated subgroups of Δ × Δ with positive first Betti number all of whose discrete faithful representations into any real semisimple Lie group are quasi-isometric embeddings. The examples of this paper are inspired by the counterexamples of Bass–Lubotzky [BL00] to Platonov’s conjecture.