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

Let K be a global function field of characteristic p, and let Γ be a finite-index subgroup of an arithmetic group defined with respect to K and such that any torsion element of Γ is a p–torsion element. We define semiduality groups, and we show that Γ is a [1p]–semiduality group if Γ 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.

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arithmetic groups, cohomology of arithmetic groups, semiduality, lamplighter group, Diestel–Leader groups
Mathematical Subject Classification 2010
Primary: 20G10
Secondary: 57M07, 57Q05
Received: 13 November 2016
Revised: 26 April 2017
Accepted: 14 July 2017
Published: 16 March 2018
Proposed: Martin Bridson
Seconded: Benson Farb, Walter Neumann
Daniel Studenmund
Department of Mathematics
University of Utah
Salt Lake City, UT
United States
Kevin Wortman
Department of Mathematics
University of Utah
Salt Lake City, UT
United States