Cocompact Lattices in Locally Pro-$p$-complete Rank 2 Kac-Moody Groups

Inna Capdeboscq; Katerina Hristova; Dmitriy Rumynin

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arXiv · 1807.07929

Cocompact Lattices in Locally Pro-$p$-complete Rank 2 Kac-Moody Groups

Inna Capdeboscq·Katerina Hristova·Dmitriy Rumynin

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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.

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Inna Capdeboscq, Katerina Hristova, Dmitriy Rumynin. 2018-07-20. Cocompact Lattices in Locally Pro-$p$-complete Rank 2 Kac-Moody Groups. https://arxiv.org/abs/1807.07929

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