Topological Complexity of Fibrations and Covering Maps

Explore the concept of topological complexity in fibrations and covering maps in this 47-minute lecture. Delve into the origins of topological complexity as a measure of manipulation complexity in mechanical devices with forward kinematic maps. Examine why this concept is not homotopy invariant for maps with singularities, and learn how the topological complexity of fibrations offers a homotopy-invariant alternative. Investigate the approximation of topological complexity for arbitrary maps using associated fibrations. Analyze the relationship between the complexity of general maps and fibrations, with a particular focus on the special case of covering maps and their complexity.