5 research outputs found
Buildings, Group Homology and Lattices
This is the author's PhD thesis, published at the Universit\"at M\"unster,
Germany in 2010. It contains a detailed description of the results of
arXiv:0903.1989, arXiv:0905.0071 and arXiv:0908.2713.Comment: 171 pages, PhD thesis, Universit\"at M\"unster, see
http://nbn-resolving.de/urn:nbn:de:hbz:6-1748954938
A geometric construction of panel-regular lattices in buildings of types ~A_2 and ~C_2
Using Singer polygons, we construct locally finite affine buildings of types
~A_2 and ~C_2 which admit uniform lattices acting regularly on panels. This
construction produces very explicit descriptions of these buildings as well as
very short presentations of the lattices. All but one of the ~C_2-buildings are
necessarily exotic. To the knowledge of the author, these are the first
presentations of lattices in buildings of type ~C_2. Integral and rational
group homology for the lattices is also calculated.Comment: 42 pages, small corrections and cleanup. Results are unchanged