A Bruhat Atlas on the Wonderful Compactification of PSO(2n)/SO(2n-1)
arXiv:1910.13545
Abstract
A stratified manifold has a Bruhat atlas on it if it can be covered with open charts such that each chart is stratified-isomorphic to an (opposite) Bruhat cell in a (usually Kac-Moody) flag manifold. In this paper, we construct an anticanonical stratification on the wonderful compactification of the symmetric space and show that the open charts are isomorphic to certain (opposite) Bruhat cells in the type flag manifold.
15 pages