Wright College Topological Robotics Symposium - Working Group
Equivariant Topological Complexities
February 5th to February 9th, 2018
Michael Farber introduced and developed the notion of topological complexity (TC) and applied this to Topological Robotics. This is a numerical invariant of Lusternik-Schnirelmann type that measures discontinuity of robot motion planning algorithms.
The topological complexity of spaces with group actions was first introduced by Hellen Colman and Mark Grant as a navigational complexity quantifier of certain mechanical problems best described by groups acting on spaces and on the other hand as a tool for obtaining estimators for the original Farber's topological complexity. Since then there have been several approaches to defining other equivariant versions of topological complexity emphasizing in different degrees one or the other of these two broad objectives.
One of the questions we are interested in is the study of Morita invariance for all the existent equivariant definitions of Topological Complexity. This is a property that comes from the groupoid context, but can be expressed in terms of group actions. Group actions are classified by Morita equivalence. The presence of that property will determine the definitive definition of TC for group actions as well as give insights on further properties in the equivariant setting, including applications.
Members:
Andres Angel
Hellen Colman
Michael Farber
Aleksandra Franc
Mark Grant
Wacław Marzantowicz
John Oprea
Yuli Rudyak
