Homotopic distance and generalized motion planning

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dc.contributor.affiliationUniversidade de Santiago de Compostela. Departamento de Matemáticasgl
dc.contributor.authorMacías Virgós, Enrique
dc.contributor.authorMosquera Lois, David
dc.contributor.authorPereira Sáez, María José
dc.date.accessioned2023-01-24T08:14:06Z
dc.date.available2023-01-24T08:14:06Z
dc.date.issued2022
dc.description.abstractWe prove that the homotopic distance between two maps defined on a manifold is bounded above by the sum of their subspace distances on the critical submanifolds of any Morse–Bott function. This generalizes the Lusternik–Schnirelmann theorem (for Morse functions) and a similar result by Farber for the topological complexity. Analogously, we prove that, for analytic manifolds, the homotopic distance is bounded by the sum of the subspace distances on any submanifold and its cut locus. As an application, we show how navigation functions can be used to solve a generalized motion planning problemgl
dc.description.peerreviewedSIgl
dc.description.sponsorshipOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The first and third authors were partially supported by MINECO Spain research project MTM2016-78647-P. The first author was partially supported by Xunta de Galicia ED431C 2019/10 with FEDER funds. The second author was partially supported by Ministerio de Ciencia, Innovación y Universidades, grant FPU17/03443 and Xunta de Galicia ED431C 2019/10 with FEDER fundsgl
dc.identifier.citationMacías-Virgós, E., Mosquera-Lois, D. & Pereira-Sáez, M.J. Homotopic Distance and Generalized Motion Planning. Mediterr. J. Math. 19, 258 (2022). https://doi.org/10.1007/s00009-022-02166-4gl
dc.identifier.doi10.1007/s00009-022-02166-4
dc.identifier.essn1660-5454
dc.identifier.issn1660-5446
dc.identifier.urihttp://hdl.handle.net/10347/29989
dc.language.isoenggl
dc.publisherSpringergl
dc.relation.projectIDinfo:eu-repo/grantAgreement/MINECO/MTM2016-78647-P/ES/gl
dc.relation.publisherversionhttps://doi.org/10.1007/s00009-022-02166-4gl
dc.rights© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/gl
dc.rightsAtribución 4.0 Internacional
dc.rights.accessRightsopen accessgl
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectMorse–Bott functiongl
dc.subjectTopological complexitygl
dc.subjectL–S categorygl
dc.subjectHomotopic distancegl
dc.subjectCut locusgl
dc.titleHomotopic distance and generalized motion planninggl
dc.typejournal articlegl
dc.type.hasVersionVoRgl
dspace.entity.typePublication
relation.isAuthorOfPublicationafea46f4-a185-4a11-a2d1-a7e30d36a5d4
relation.isAuthorOfPublication.latestForDiscoveryafea46f4-a185-4a11-a2d1-a7e30d36a5d4

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