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