Piecewise linear sheaves

Masaki Kashiwara; Pierre Schapira

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arXiv · 1805.00349

Piecewise linear sheaves

Masaki Kashiwara·Pierre Schapira

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Abstract

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.

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Masaki Kashiwara, Pierre Schapira. 2018-04-30. Piecewise linear sheaves. https://arxiv.org/abs/1805.00349

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