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.

arXiv comment47 pages, 1 figure, v2: minor revision, v3: final accepted version, some typos corrected

References in corpus (10)

• Derived Algebraic Geometry V: Structured Spaces
• The fundamental category of a stratified space
• Exit paths and constructible stacks
• Endotrivial modules for finite groups via homotopy theory
• L-modules and micro-support
• Cyclic structures and broken cycles
• Lectures on controlled topology: mapping cylinder neighborhoods
• On the homotopy type of the Deligne-Mumford compactification
• The fundamental group of reductive Borel-Serre and Satake compactifications
• 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