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arXiv · 2012.10777

The stratified homotopy type of the reductive Borel-Serre compactification

Mikala Ørsnes Jansen
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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.

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Mikala Ørsnes Jansen. 2020-12-19. The stratified homotopy type of the reductive Borel-Serre compactification. https://doi.org/10.1093/imrn%2Frnac289

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