Cocompact lattices in locally pro-p-complete rank 2 Kac-Moody groups

Capdeboscq, I.; Hristova, K.; Rumynin, D. A.

doi:10.1070/SM9311

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Cocompact lattices in locally pro-p-complete rank 2 Kac-Moody groups

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Rumynin, D. A.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1070/SM9311
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arXiv:1807.07929.pdf
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Citation

Capdeboscq, I., Hristova, K., & Rumynin, D. A. (2020). Cocompact lattices in locally pro-p-complete rank 2 Kac-Moody groups. Sbornik. Mathematics, 211(8), 1065-1079. doi:10.1070/SM9311.

Cite as: https://hdl.handle.net/21.11116/0000-0007-8171-7

Abstract

We initiate an investigation of lattices in a new class of locally compact
groups, so called locally pro-$p$-complete Kac-Moody groups. We discover that
in rank 2 their cocompact lattices are particularly well-behaved: under mild
assumptions, a cocompact lattice in this completion contains no elements of
order $p$. This statement is still an open question for the
Caprace-R\'emy-Ronan completion. Using this, modulo results of Capdeboscq and
Thomas, we classify edge-transitive cocompact lattices and describe a cocompact
lattice of minimal covolume.