Summary: The geometries studied in this paper are obtained from buildings of spherical type by removing all chambers at non-maximal distance from a given element or flag. I consider a number of special cases of the above construction chosen among those which most frequently appear in the literature, proving that the resulting geometry is always simply connected but for three cases of small rank defined over $GF(2)$ and $GF(4)$. I also compute the universal cover in those exceptional cases.
@article{JAC_2003__18_3_a2,
author = {Pasini, Antonio},
title = {Universal covers of geometries of far away type},
journal = {Journal of Algebraic Combinatorics},
pages = {211--243},
publisher = {mathdoc},
volume = {18},
number = {3},
year = {2003},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JAC_2003__18_3_a2/}
}
TY - JOUR
AU - Pasini, Antonio
TI - Universal covers of geometries of far away type
JO - Journal of Algebraic Combinatorics
PY - 2003
SP - 211
EP - 243
VL - 18
IS - 3
PB - mathdoc
UR - http://geodesic.mathdoc.fr/item/JAC_2003__18_3_a2/
LA - en
ID - JAC_2003__18_3_a2
ER -
%0 Journal Article
%A Pasini, Antonio
%T Universal covers of geometries of far away type
%J Journal of Algebraic Combinatorics
%D 2003
%P 211-243
%V 18
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2003__18_3_a2/
%G en
%F JAC_2003__18_3_a2
Pasini, Antonio. Universal covers of geometries of far away type. Journal of Algebraic Combinatorics, Tome 18 (2003) no. 3, pp. 211-243. http://geodesic.mathdoc.fr/item/JAC_2003__18_3_a2/