{"title":"Proper topological complexity","authors":"Jose M. Garcia-Calcines, Aniceto Murillo","doi":"arxiv-2407.16679","DOIUrl":null,"url":null,"abstract":"We introduce and study the proper topological complexity of a given\nconfiguration space, a version of the classical invariant for which we require\nthat the algorithm controlling the motion is able to avoid any possible choice\nof ``unsafe'' area. To make it a homotopy functorial invariant we characterize\nit as a particular instance of the exterior sectional category of an exterior\nmap, an invariant of the exterior homotopy category which is also deeply\nanalyzed.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.16679","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce and study the proper topological complexity of a given
configuration space, a version of the classical invariant for which we require
that the algorithm controlling the motion is able to avoid any possible choice
of ``unsafe'' area. To make it a homotopy functorial invariant we characterize
it as a particular instance of the exterior sectional category of an exterior
map, an invariant of the exterior homotopy category which is also deeply
analyzed.
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