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

Essert, Jan¹

¹Mathematisches Institut, Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany

Algebraic and Geometric Topology, Tome 13 (2013) no. 3, pp. 1531-1578

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.1531

Classification : 20E42, 20F65, 22E40, 20J06
Keywords: affine buildings, lattices, exotic buildings, group theory, complexes of groups

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