{"title":"The reach of subsets of manifolds","authors":"J. Boissonnat, M. Wintraecken","doi":"10.1007/s41468-023-00116-x","DOIUrl":"https://doi.org/10.1007/s41468-023-00116-x","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"619 - 641"},"PeriodicalIF":0.0,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42619158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vietoris thickenings and complexes are weakly homotopy equivalent","authors":"P. Gillespie","doi":"10.1007/s41468-023-00135-8","DOIUrl":"https://doi.org/10.1007/s41468-023-00135-8","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42604295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michał Lipiński, Jacek Kubica, Marian Mrozek, Thomas Wanner
{"title":"Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces.","authors":"Michał Lipiński, Jacek Kubica, Marian Mrozek, Thomas Wanner","doi":"10.1007/s41468-022-00102-9","DOIUrl":"10.1007/s41468-022-00102-9","url":null,"abstract":"<p><p>We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector fields introduced in Mrozek (Found Comput Math 17(6):1585-1633, 2017). The generalization is threefold. First, we drop the restraining assumption in Mrozek (Found Comput Math 17(6):1585-1633, 2017) that every multivector must have a unique maximal element. Second, we define the dynamical system induced by the multivector field in a less restrictive way. Finally, we also change the setting from Lefschetz complexes to finite topological spaces. Formally, the new setting is more general, because every Lefschetz complex is a finite topological space, but the main reason for switching to finite topologcial spaces is because the latter better explain some peculiarities of combinatorial topological dynamics. We define isolated invariant sets, isolating neighborhoods, Conley index and Morse decompositions. We also establish the additivity property of the Conley index and the Morse inequalities.</p>","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 2","pages":"139-184"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10181983/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9474937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On merge trees and discrete Morse functions on paths and trees","authors":"Julian Brüggemann","doi":"10.1007/s41468-022-00101-w","DOIUrl":"https://doi.org/10.1007/s41468-022-00101-w","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"103 - 138"},"PeriodicalIF":0.0,"publicationDate":"2022-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53194412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Ethier, Patrizio Frosini, Nicola Quercioli, Francesca Tombari
{"title":"Geometry of the matching distance for 2D filtering functions","authors":"M. Ethier, Patrizio Frosini, Nicola Quercioli, Francesca Tombari","doi":"10.1007/s41468-023-00128-7","DOIUrl":"https://doi.org/10.1007/s41468-023-00128-7","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"815 - 830"},"PeriodicalIF":0.0,"publicationDate":"2022-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45893464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Topological perplexity of feedback stabilization","authors":"yuliy baryshnikov","doi":"10.1007/s41468-022-00098-2","DOIUrl":"https://doi.org/10.1007/s41468-022-00098-2","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"75 - 87"},"PeriodicalIF":0.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47222534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: The space of barcode bases for persistence modules","authors":"Emile Jacquard, Vidit Nanda, U. Tillmann","doi":"10.1007/s41468-022-00097-3","DOIUrl":"https://doi.org/10.1007/s41468-022-00097-3","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"31 - 31"},"PeriodicalIF":0.0,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48119943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maximal persistence in random clique complexes","authors":"Ayat Ababneh, Matthew Kahle","doi":"10.1007/s41468-023-00131-y","DOIUrl":"https://doi.org/10.1007/s41468-023-00131-y","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44768423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}