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

TL;DR

This paper determines the Lusternik-Schnirelmann category of the homotopy cofiber of the diagonal map and the topological complexity of non-orientable surfaces, providing new insights into their topological invariants.

Contribution

It establishes the exact values of the Lusternik-Schnirelmann category and topological complexity for non-orientable surfaces, extending previous knowledge in topological invariants.

Findings

Lusternik-Schnirelmann category of the homotopy cofiber equals three.

Topological complexity of non-orientable surfaces with genus > 3 is four.

Provides new calculations for topological invariants of 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.