Persistent topological complexity and persistent zero-divisor-cup-length are defined, shown stable under homotopy interleaving and Vietoris-Rips perturbations, and used to recover a Gromov-Hausdorff lower bound of pi/6 for RP^n versus a wedge of spheres.
[Cor+03] Octavian Cornea, Gregory Lupton, John Oprea, Daniel Tanr´ e, et al.Lusternik-Schnirelmann category
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Persistence and Topological Complexity
Persistent topological complexity and persistent zero-divisor-cup-length are defined, shown stable under homotopy interleaving and Vietoris-Rips perturbations, and used to recover a Gromov-Hausdorff lower bound of pi/6 for RP^n versus a wedge of spheres.