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

Abstract

We show that the Lusternik-Schnirelmann category of the homotopy cofiber of the diagonal map for non-orientable surfaces equals three. Also, we prove that the topological complexity of non-orientable surfaces of genus $>3$ is four.

In the version 1 title was "On the homotopy cofiber of the diagonal map for non-orientable surfaces". In the version 3 case of the Klein bottle is added. The version 4 covers all non-orientable surfaces but it contains a crucial error. Version 5 covers non-orientable surfaces of all genera except 3 but the proof in the case g=2 has a gap. The current version covers the case of g>3

References in corpus (2)

• On the Berstein-Svarc Theorem in dimension 2
• Weak sectional category