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Homotopic distance for maps which is defined by Macias-Virgos and Mosquera-Lois is both related to topological complexity and Lusternik-Schnirelmann category [2]. In this talk, we will consider the higher homotopic distance. We will introduce some of its properties and give its relation with the higher topological complexity and the Lusternik-Schnirelmann category. This is a joint work with Tane Vergili.
References:
[1] M. Farber, Topological Complexity of Motion Planning, Discrete Comput. Geom. 29 (2003), No. 2, 211-221.
[2] E. Macias-Virgos, D. Mosquera-Lois, Homotopic Distance between Maps, preprint. arXiv: 1810.12591v2.
[3] Y. Rudyak, On higher analogs of topological complexity, Topology Appl. 157 (2010) 916-920. Erratum: Topology Appl. 157 (2010) 11-18.