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Stratifications of real vector spaces from constructible sheaves with conical microsupport

Stratifications of real vector spaces from constructible sheaves with conical microsupport Interpreting the syzygy theorem for tame modules over posets in the setting of derived categories of subanalytically constructible sheaves proves two conjectures due to Kashiwara and Schapira concerning the existence of stratifications of real vector spaces that play well with sheaves having microsupport in a given cone or, equivalently, sheaves in the corresponding conic topology. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied and Computational Topology Springer Journals

Stratifications of real vector spaces from constructible sheaves with conical microsupport

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References (36)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
2367-1726
eISSN
2367-1734
DOI
10.1007/s41468-023-00112-1
Publisher site
See Article on Publisher Site

Abstract

Interpreting the syzygy theorem for tame modules over posets in the setting of derived categories of subanalytically constructible sheaves proves two conjectures due to Kashiwara and Schapira concerning the existence of stratifications of real vector spaces that play well with sheaves having microsupport in a given cone or, equivalently, sheaves in the corresponding conic topology.

Journal

Journal of Applied and Computational TopologySpringer Journals

Published: Sep 1, 2023

Keywords: Subanalytic constructible sheaf; Conic topology; Syzygy theorem; Multiparameter persistent homology; Tame poset module; Conical microsupport; Primary: 32S60; 32B20; 14F07; 55N31; 62R40; 32B25; 13D02; 13E99; 52B99; 06F20; 06F05; 20M25; 05E40; 13A02; 13P20; 68W30; 13P25; 68T09; Secondary: 06A11; 06A07; 14P10; 13C99; 05E16; 62R01; 13F99; 06B35; 20M14; 22A25

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