Homotopic distance as introduced by Macias-Virgos and Mosquera-Lois in [2] can be realised as a generalisation of topological complexity (TC) and Lusternik Schnirelmann category (cat). In this talk, we will introduce a simplicial analogue (in the sense of Gonzalez as in [1] and as given in [3]) of homotopic distance and show that it has a relation with simplicial complexity (SC) as homotopic distance has with TC. We will also have a quick glance at contiguity distance as introduced in [2] and improved in [4].

References

[1] J. Gonzalez, Simplicial Complexity: Piecewise Linear Motion Planning in Robotics, New York Journal of Mathematics 24 (2018), 279-292.

[2] E. Macias-Virgos, D. Mosquera-Lois, Homotopic Distance between Maps, Mathematical Proceedings of the Cambridge Philosophical Society (2021), 1-21.

[3] C. Ortiz, A. Lara, J. Gonzalez, A. Borat, A randomized greedy algorithm for piecewise linear motion planning, Mathematics, Vol 9, Issue 19 (2021).

[4] A. Borat, M. Pamuk, T. Vergili, Contiguity Distance between Simplicial Maps, submitted, 2020. ArXiv: 2012.10627.