Real monodromy action
For researchers in kinematics and real algebraic geometry, this provides a new invariant for real solution structures, though the contribution is incremental as it extends existing monodromy concepts to the real case with limited generality.
The paper introduces a real monodromy structure for parameterized polynomial systems, which captures tiered characteristics of real solutions over real parameter spaces, and applies it to a kinematics example to summarize how loops in leg lengths cause a mechanism to change poses.
The monodromy group is an invariant for parameterized systems of polynomial equations that encodes structure of the solutions over the parameter space. Since the structure of real solutions over real parameter spaces are of interest in many applications, real monodromy action is investigated here. A naive extension of monodromy action from the complex numbers to the real numbers is shown to be very restrictive. Therefore, we define a real monodromy structure which need not be a group but contains tiered characteristics about the real solutions. This real monodromy structure is applied to an example in kinematics which summarizes all the ways performing loops parameterized by leg lengths can cause a mechanism to change poses.