Homotopic distance and generalized motion planning
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http://hdl.handle.net/2183/32200
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Homotopic distance and generalized motion planningData
2022-10-18Cita bibliográfica
Macías-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/s00009-022-02166-4
Resumo
[Abstract]: We 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 problem.
Palabras chave
Morse–Bott function
Topological complexity
L–S category
Homotopic distance
Cut locus
Topological complexity
L–S category
Homotopic distance
Cut locus
Descrición
Attribution 4.0 International
Versión do editor
ISSN
1660-5446