The topological complexity of non-$k$-equal spaces

Abstract

The non-k-equal spaces are a type of generalization of configuration spaces where we allow less than k collisions or equalities in the coordinates of n-tuples. In this talk, I will describe the techniques for finding the Lusternik-Schnirelmann category and topological complexity for non-k-spaces over n-tuples of real numbers. Also, some conjectures about extending these results for the case of k parabolic arrangements will be presented.