turkmath.org

In this talk, I will revisit the concept of effectual and effective topological complexity (TC) in the context of sequential motion planning. These invariants provide a natural context to incorporate group actions into the study of the motion planning problem. Related to these invariants, I will talk about a third version of TC that incorporates the group action into its planners, which we call orbital topological complexity. I will discuss how they relate to each other and to the TC of the quotient space. I will also present some calculations for actions of the group of order two on orientable surfaces and spheres.