Pub Date : 2023-03-02DOI: 10.1007/s41468-023-00135-8
P. Gillespie
{"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}
Pub Date : 2023-01-01Epub Date: 2022-10-05DOI: 10.1007/s41468-022-00102-9
Michał Lipiński, Jacek Kubica, Marian Mrozek, Thomas Wanner
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.
我们对Mrozek（Found Comput Math 17（6）：1585-16332017）中引入的组合多向量场的Conley Morse Forman理论进行了推广和推广。概括有三个方面。首先，我们放弃了Mrozek（Found Comput Math 17（6）:1585-16332017）中的约束假设，即每个多向量都必须具有唯一的极大元素。其次，我们以一种限制较少的方式定义了由多矢量场诱导的动力系统。最后，我们还将勒夫谢兹复形的设置改为有限拓扑空间。形式上，新的设置更一般，因为每个Lefschetz复形都是有限拓扑空间，但切换到有限拓扑空间的主要原因是后者更好地解释了组合拓扑动力学的一些特性。我们定义了孤立不变集、孤立邻域、康利指数和Morse分解。我们还建立了Conley指数和Morse不等式的可加性。
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Pub Date : 2022-11-26DOI: 10.1007/s41468-022-00101-w
Julian Brüggemann
{"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}
Pub Date : 2022-10-30DOI: 10.1007/s41468-023-00128-7
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}
Pub Date : 2022-10-17DOI: 10.1007/s41468-022-00098-2
yuliy baryshnikov
{"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}
Pub Date : 2022-09-26DOI: 10.1007/s41468-022-00097-3
Emile Jacquard, Vidit Nanda, U. Tillmann
{"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}
Pub Date : 2022-09-13DOI: 10.1007/s41468-023-00131-y
Ayat Ababneh, Matthew Kahle
{"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}
Pub Date : 2022-07-17DOI: 10.1007/s41468-023-00114-z
D. Blanc, N. Shvalb
{"title":"Symmetric configuration spaces of linkages","authors":"D. Blanc, N. Shvalb","doi":"10.1007/s41468-023-00114-z","DOIUrl":"https://doi.org/10.1007/s41468-023-00114-z","url":null,"abstract":"","PeriodicalId":73600,"journal":{"name":"Journal of applied and computational topology","volume":"7 1","pages":"527 - 569"},"PeriodicalIF":0.0,"publicationDate":"2022-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45531875","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}
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