#### Volume 22, issue 3 (2018)

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Semidualities from products of trees

### Daniel Studenmund and Kevin Wortman

Geometry & Topology 22 (2018) 1717–1758
##### Abstract

Let $K$ be a global function field of characteristic $p$, and let $\Gamma$ be a finite-index subgroup of an arithmetic group defined with respect to $K$ and such that any torsion element of $\Gamma$ is a $p$–torsion element. We define semiduality groups, and we show that $\Gamma$ is a $ℤ\left[1∕p\right]$–semiduality group if $\Gamma$ acts as a lattice on a product of trees. We also give other examples of semiduality groups, including lamplighter groups, Diestel–Leader groups, and countable sums of finite groups.

##### Keywords
arithmetic groups, cohomology of arithmetic groups, semiduality, lamplighter group, Diestel–Leader groups
##### Mathematical Subject Classification 2010
Primary: 20G10
Secondary: 57M07, 57Q05