Higher topological complexity of Seifert fibred manifolds

In this article, we investigate the higher topological complexity of oriented Seifert fibred manifolds that are Eilenberg–MacLane spaces $K(G,1)$ with infinite fundamental group G . We first refine the cohomological lower bounds for higher topological complexity by introducing the notion of higher topological complexity weights. As an application, we show that the rᵗʰ topological complexity of these manifolds lies in \3r-1, 3r, 3r+1\ , and characterize large families where the value is $3r$ or $3r+1$ . Additionally, we establish a sufficient condition for higher topological complexity to be exactly $3r$ when the base surface is orientable and aspherical. Finally, we show that the higher topological complexity of the wedge of finitely many closed, orientable, aspherical $3$ -manifolds is exactly $3r+1$ .