Topology Seminar: Enrique Torres

Topological Complexity (TC) of a space is a concept motivated by the motion planning problem in Robotics. This turns out to be a homotopy invariant, closely related to Lusternik-Schnirelmann category (LS-cat). In fact, TC has proved more delicate than LS-cat given its relationship with some difficult problems in Algebraic Topology such as the Immersion Problem for Projective Spaces.

In this talk we will discuss basic properties and examples of TC. We will also discuss some recent progress on the computation of TC of some homogeneous spaces, and talk about some new techniques to compute TC based on Hopf-like invariants.