Topological complexity and the homotopy cofibre of the diagonal map

Details Topological complexity and the homotopy cofibre of the diagonal map Topological complexity and the homotopy cofibre of the diagonal map

2011-06-24

arxiv.org/abs/1106.4943v2

Mathematics

Algebraic Topology

26 pages

Scientific paper

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 $\Delta_X:X\rightarrow X\times X.$ 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.

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