{"title":"Parametrized topological complexity of spherical fibrations over spheres","authors":"Yuki Minowa","doi":"arxiv-2406.17227","DOIUrl":null,"url":null,"abstract":"Parametrized topological complexity is a homotopy invariant that represents\nthe degree of instability of motion planning problem that involves external\nconstraints. We consider the parametrized topological complexity in the case of\nspherical fibrations over spheres. We explicitly compute a lower bound in terms\nof weak category and determine the parametrized topological complexity of some\nspherical fibrations.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"88 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-25","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-2406.17227","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
Parametrized topological complexity is a homotopy invariant that represents
the degree of instability of motion planning problem that involves external
constraints. We consider the parametrized topological complexity in the case of
spherical fibrations over spheres. We explicitly compute a lower bound in terms
of weak category and determine the parametrized topological complexity of some
spherical fibrations.
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