Homotopic distance and generalized motion planning
![Thumbnail](/dspace/bitstream/handle/2183/32200/MaciasVirgos_Enrique_2022_Homotopic-distance-generalized-motion-planning.pdf.jpg?sequence=5&isAllowed=y)
Use this link to cite
http://hdl.handle.net/2183/32200
Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by/3.0/es/
Collections
- GI-XDA - Artigos [13]
Metadata
Show full item recordTitle
Homotopic distance and generalized motion planningDate
2022-10-18Citation
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
Abstract
[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.
Keywords
Morse–Bott function
Topological complexity
L–S category
Homotopic distance
Cut locus
Topological complexity
L–S category
Homotopic distance
Cut locus
Description
Attribution 4.0 International
Editor version
ISSN
1660-5446