Online seminar, U. Haifa Topology & Geometry seminar on December 27, 2020
A recording of the talk is available here.
Topology & Geometry Seminar
Speaker: David Recio-Mitter, Lehigh University
Topic: Geodesic complexity of motion planning
Place: This is an online seminar. Please email David Blanc “blanc at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Sunday, December 27, 2020
Geodesic complexity of motion planning The topological complexity TC(X) of a space X was introduced in 2003 by Farber to measure the instability of robot motion planning in X. The motion is not required to be along shortest paths in that setting. We define a new version of topological complexity in which we require the robot to move along shortest paths (more specifically geodesics), which we call the geodesic complexity GC(X). In order to study GC(X) we introduce the total cut locus.
We show that the geodesic complexity is sensitive to the metric and in general differs from the topological complexity, which only depends on the homotopy type of the space. We also show that in some cases both numbers agree.