A geometric construction of panel-regular lattices for buildings of types Ã2 and C̃2

Essert, Jan

doi:10.2140/agt.2013.13.1531

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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

DOI: 10.2140/agt.2013.13.1531

Abstract

Using Singer polygons, we construct locally finite affine buildings of types $Ã_{2}$ and ${\tilde{C}}_{2}$ that admit uniform lattices acting regularly on panels. For type $Ã_{2}$ , these cover all possible buildings admitting panel-regular lattices. All but one of the ${\tilde{C}}_{2}$ –buildings are necessarily exotic. To the knowledge of the author, these are the first presentations of lattices for buildings of type ${\tilde{C}}_{2}$ . 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/

Volume 13, issue 3 (2013)