Exit paths and constructible stacks

By David Treumann. Compositio Mathematica, 2007

78 citations recorded by the source corpus.

Abstract 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.

Subfields: Artificial Intelligence, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/812d97f965a38be0f4286a8883727aa3a41b825b

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Citations in the corpus

Perverse sheaves over real hyperplane arrangements (2014, unknown): “for arbitrary stratifications; see [41].”
The fundamental category of a stratified space (2008, unknown): “MacPherson’s ideas were published and extended by Treumann [ Tre07 ] in which he refers to paths which wind outwards as exit paths.”
Spaces of smooth embeddings and configuration categories (2015, background): “pace Z by setting Zn = Y for all n. This Zis a complete Segal space. We can also view it as (the nerve of) a topological category with space of objects Y and space of morphisms Y. (v) (See also [45], [41]) Let Zbe a stratiﬁed space; that is, Zis a space equipped with a locally ﬁnite partition into l”