The Stratified Homotopy Type of the Reductive Borel–Serre Compactification

Abstract

Abstract We identify the exit path $\infty $-category of the reductive Borel–Serre compactification as the nerve of a $1$-category defined purely in terms of rational parabolic subgroups and their unipotent radicals. As immediate consequences, we identify the fundamental group of the reductive Borel–Serre compactification, recovering a result of Ji–Murty–Saper–Scherk, and we obtain a combinatorial incarnation of constructible complexes of sheaves on the reductive Borel–Serre compactification as elements in a derived functor category.