Piecewise Linear Sheaves

On a finite-dimensional real vector space, we give a microlocal characterization of (derived) piecewise linear sheaves (PL sheaves) and prove that the triangulated category of such sheaves is generated by sheaves associated with convex polyhedra. We then give a similar theorem for PL $\gamma $-sheav...

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Bibliographic Details
Published in:International mathematics research notices 2021-08, Vol.2021 (15), p.11565-11584
Main Authors: Kashiwara, Masaki, Schapira, Pierre
Format: Article
Language:English
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Summary:On a finite-dimensional real vector space, we give a microlocal characterization of (derived) piecewise linear sheaves (PL sheaves) and prove that the triangulated category of such sheaves is generated by sheaves associated with convex polyhedra. We then give a similar theorem for PL $\gamma $-sheaves, that is, PL sheaves associated with the $\gamma $-topology, for a closed convex polyhedral proper cone $\gamma $. Our motivation is that convex polyhedra may be considered as building blocks for higher dimensional barcodes.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnz145