Title: Relative Topological Complexity for Pairs of Right-Angled Artin Groups
Speaker: Robert Short (Lehigh University)
Abstract: Topological complexity is a homotopy invariant introduced by Michael Farber in the early 2000s. Denoted $TC(X)$, it counts the smallest size of a continuous motion planning algorithm on X. In this sense, it solves optimally the problem of continuous motion planning in a given topological space. In topological robotics, a part of applied algebraic topology, several variants of $TC$ are studied. In a recent paper, I introduced the relative topological complexity of a pair of spaces $(X, Y )$ where $Y \subset X$. Denoted $TC(X, Y )$, this counts the smallest size of motion planning algorithms that plan from $X$ to $Y$.
Right-angled Artin groups have grown in importance lately with their connection to braid groups and their connection to real-world robotics problems. In this talk, we will present the background needed to compute the relative topological complexity of pairs of right-angled Artin groups and hopefully discuss the details of the optimal motion planner involved.'
Seminar URL: http://research.math.osu.edu/topology
