Directed topological complexity of spheres

Ayşe Borat
Bursa Technical University

Abstract: Topological complexity is a homotopy invariant which measures how far a space away from
admitting a motion planning algorithm [2]. A new variant of topological complexity given through
directed paths is introduced by Goubault, Sagnier and Farber in [3]. This new concept is useful for
classifying directed spaces.
In this talk, I will give a brief introduction to usual topological complexity and directed topological
complexity, and I will discuss directed topological complexity of directed n-spheres [1]. This is a joint
work with Mark Grant.

References
[1] A. Borat, M. Grant, Directed topological complexity of spheres, submitted. arXiv:1810.00339.
[2] M. Farber, Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003), no. 2, 211—221.
[3] E. Goubault, A. Sagnier, M. Farber, Directed topological complexity, submitted. arXiv:1812.09382.