Topological complexity of Milnor fibration

Abstract

In this paper we discover a connection between the Milnor fibration theory and current research trends in topological robotics. The configuration space and workspace are often described as subspaces of some Euclidean spaces. The work map is a continuous map which assigns to each state of the configuration space the position of the end-effector at that state. The tasking planning problem consists in study the complexity and design of algorithms controlling the task performed by the robot manipulator. We study the tasking planning problem for the Milnor fibration of analytic map germs. We see that the tasking planning algorithms strongly depend of the Milnor fibration theorem. We conjecture that the topological complexity of Milnor fibration coincides with the topological complexity of its base.