The stratified homotopy type of the reductive Borel-Serre compactification

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 an immediate consequence, 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.

47 pages, 1 figure, v2: minor revision, v3: final accepted version, some typos corrected

References in corpus (3)

• Derived Algebraic Geometry V: Structured Spaces
• Cyclic structures and broken cycles
• The reductive Borel-Serre compactification as a model for unstable algebraic K-theory

Cited by in corpus (3)

• Stratified homotopy theory of topological $\infty$-stacks: a toolbox
• Compact sheaves on a locally compact space
• A stratified Kan-Quillen equivalence