Verdier duality on conically smooth stratified spaces

Volpe, Marco

doi:10.2140/agt.2025.25.919

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Verdier duality on conically smooth stratified spaces

Marco Volpe

Algebraic & Geometric Topology 25 (2025) 919–950

DOI: 10.2140/agt.2025.25.919

Abstract

We prove a duality for constructible sheaves on conically smooth stratified spaces. We consider sheaves with values in a stable and bicomplete $\infty$ -category equipped with a closed symmetric monoidal structure, and in this setting constructible means locally constant along strata and with dualizable stalks. The crucial point where we need to employ the geometry of conically smooth structures is in showing that Lurie’s version of Verdier duality restricts to an equivalence between constructible sheaves and cosheaves: this requires a computation of the exit paths $\infty$ -category of a compact stratified space, which we obtain via resolution of singularities.

Keywords

constructible sheaves, finite infinity categories, stratified spaces, conically smooth, Verdier duality, dualizing complex

Mathematical Subject Classification

Primary: 18N60, 54B40, 57N80, 57P05

References

Publication

Received: 12 December 2022

Revised: 10 December 2023

Accepted: 4 February 2024

Published: 16 May 2025

Authors

Marco Volpe
Department of Mathematics University of Toronto Toronto, ON Canada

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Volume 25, issue 2 (2025)