Volume 13, issue 3 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A geometric construction of panel-regular lattices for buildings of types $\wtilde A_2$ and $\wtilde C_2$

Jan Essert

Algebraic & Geometric Topology 13 (2013) 1531–1578
Abstract

Using Singer polygons, we construct locally finite affine buildings of types Ã2 and C̃2 that admit uniform lattices acting regularly on panels. For type Ã2, these cover all possible buildings admitting panel-regular lattices. All but one of the C̃2–buildings are necessarily exotic. To the knowledge of the author, these are the first presentations of lattices for buildings of type C̃2. Integral and rational group homology for the lattices is also calculated.

Keywords
affine buildings, lattices, exotic buildings, group theory, complexes of groups
Mathematical Subject Classification 2010
Primary: 20E42, 20F65, 22E40
Secondary: 20J06
References
Publication
Received: 9 August 2012
Revised: 17 October 2012
Accepted: 19 October 2012
Published: 9 May 2013
Authors
Jan Essert
Mathematisches Institut, Universität Münster
Einsteinstr. 62
D-48149 Münster
Germany
http://jan.essert.name/