RT Journal Article
T1 Homotopic distance and generalized motion planning
A1 Macías Virgós, Enrique
A1 Mosquera Lois, David
A1 Pereira Sáez, María José
K1 Morse–Bott function
K1 Topological complexity
K1 L–S category
K1 Homotopic distance
K1 Cut locus
AB 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
PB Springer
SN 1660-5446
YR 2022
FD 2022
LK http://hdl.handle.net/10347/29989
UL http://hdl.handle.net/10347/29989
LA eng
NO 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
NO Open 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 funds
DS Minerva
RD 22 abr 2026