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Exit paths and constructible stacks

Part of: Singularities

Published online by Cambridge University Press:  21 September 2009

David Treumann
David Treumann*
Affiliation:
127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN 55455, USA (email: [email protected])
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Abstract

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For a Whitney stratification S of a space X (or, more generally, a topological stratification in the sense of Goresky and MacPherson) we introduce the notion of an S-constructible stack of categories on X. The motivating example is the stack of S-constructible perverse sheaves. We introduce a 2-category EP≤2(X,S), called the exit-path 2-category, which is a natural stratified version of the fundamental 2-groupoid. Our main result is that the 2-category of S-constructible stacks on X is equivalent to the 2-category of 2-functors 2Funct(EP≤2(X,S),Cat) from the exit-path 2-category to the 2-category of small categories.

Keywords

stratificationsconstructible sheavesperverse sheavesstacks

MSC classification

Secondary: 32S60: Stratifications; constructible sheaves; intersection cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 6 , November 2009 , pp. 1504 - 1532
Copyright
Copyright © Foundation Compositio Mathematica 2009

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