The topological complexity and the homotopy cofiber of the diagonal map for non-orientable surfaces

Dranishnikov, Alexander

doi:10.1090/proc/13219

The topological complexity and the homotopy cofiber of the diagonal map for non-orientable surfaces
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Proc. Amer. Math. Soc. 144 (2016), 4999-5014 Request permission

Abstract:

We show that the Lusternik-Schnirelmann category of the homotopy cofiber of the diagonal map of non-orientable surfaces equals three.

Also, we prove that the topological complexity of non-orientable surfaces of genus $> 4$ is four.

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