An Upper Bound on the Sequential Topological Complexity

Explore the concept of sequential topological complexity and its applications in robot motion planning through this 47-minute lecture from the Applied Algebraic Topology Network. Delve into Farber's introduction of topological complexity as a measure of complexity in robot motion planning within configuration spaces. Examine Rudyak's higher analogue, known as higher/sequential topological complexity. Learn about the newly defined notion of higher subspace topological complexity and discover an upper bound on the higher topological complexity of total spaces of fibrations. Understand how this upper bound can improve the dimensional upper bound on higher topological complexity in the presence of group actions. Apply these concepts to compute the higher topological complexity of several higher-dimensional lens spaces, gaining practical insights into sequential motion planning in complex topological spaces.