{"day":"19","article_number":"108068","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"date_updated":"2025-09-10T07:41:26Z","author":[{"first_name":"Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam"},{"full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0464-3823","last_name":"Draganov","first_name":"Ondrej"}],"volume":229,"OA_place":"publisher","article_type":"original","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35","quality_controlled":"1","date_published":"2025-08-19T00:00:00Z","date_created":"2025-09-10T05:40:09Z","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"epub_ahead","doi":"10.1016/j.jpaa.2025.108068","publisher":"Elsevier","has_accepted_license":"1","OA_type":"hybrid","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"18981"}]},"title":"Discrete microlocal Morse theory","type":"journal_article","corr_author":"1","arxiv":1,"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"citation":{"chicago":"Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” <i>Journal of Pure and Applied Algebra</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">https://doi.org/10.1016/j.jpaa.2025.108068</a>.","mla":"Brown, Adam, and Ondrej Draganov. “Discrete Microlocal Morse Theory.” <i>Journal of Pure and Applied Algebra</i>, vol. 229, no. 10, 108068, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">10.1016/j.jpaa.2025.108068</a>.","ama":"Brown A, Draganov O. Discrete microlocal Morse theory. <i>Journal of Pure and Applied Algebra</i>. 2025;229(10). doi:<a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">10.1016/j.jpaa.2025.108068</a>","short":"A. Brown, O. Draganov, Journal of Pure and Applied Algebra 229 (2025).","ista":"Brown A, Draganov O. 2025. Discrete microlocal Morse theory. Journal of Pure and Applied Algebra. 229(10), 108068.","ieee":"A. Brown and O. Draganov, “Discrete microlocal Morse theory,” <i>Journal of Pure and Applied Algebra</i>, vol. 229, no. 10. Elsevier, 2025.","apa":"Brown, A., &#38; Draganov, O. (2025). Discrete microlocal Morse theory. <i>Journal of Pure and Applied Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jpaa.2025.108068\">https://doi.org/10.1016/j.jpaa.2025.108068</a>"},"language":[{"iso":"eng"}],"PlanS_conform":"1","intvolume":"       229","issue":"10","month":"08","ddc":["510"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jpaa.2025.108068"}],"abstract":[{"lang":"eng","text":"We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category of sheaves on a poset with the Alexandrov topology. We prove that each bounded complex of sheaves on a finite poset admits a unique (up to isomorphism of complexes) minimal injective resolution, and we provide algorithms for computing minimal injective resolution of an injective complex, as well as several useful functors between derived categories of sheaves. For the constant sheaf on a simplicial complex, we give asymptotically tight bounds on the complexity of computing the minimal injective resolution using those algorithms. Our main result is a novel definition of the discrete microsupport of a bounded complex of sheaves on a finite poset. We detail several foundational properties of the discrete microsupport, as well as a microlocal generalization of the discrete homological Morse theorem and Morse inequalities."}],"ec_funded":1,"article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"external_id":{"arxiv":["2209.14993"]},"oa_version":"Published Version","publication":"Journal of Pure and Applied Algebra","year":"2025","publication_identifier":{"issn":["0022-4049"]},"_id":"20323"}