Topological complexity and the homotopy cofibre of the diagonal map

Abstract

In this paper, we establish some relationships between the topological complexity of a space X and the category of CΔX, the homotopy cofibre of the diagonal map ΔX: X → X × X. In particular, we prove the equality of the two invariants for several classes of spaces including the spheres, the H-spaces, the real and complex projective spaces and almost all (standard) lens spaces. © 2012 Springer-Verlag.