Topological complexity and the homotopy cofibre of the diagonal map

Abstract

In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{{\Delta }_X},$ the homotopy cofibre of the diagonal map ${\Delta }_X:X\to X\times X.$ We establish 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 the (standard) lens spaces.

arXiv comment26 pages

References in corpus (1)

• The sectional category of a map