2024/04/04 by Navnath Daundkar, Daundkar, Navnath
Mathematics · #55M30 #55P20 #55R10 #55S40 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2404.03757
openalex publication_date 2024/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study the sequential analogue of Grant's parametrized topological complexity of group epimorphisms, which generalizes the sequential topological complexity of groups. We derive bounds for sequential parametrized topological complexity based on the cohomological dimension of certain subgroups, thereby extending the corresponding bounds for sequential topological complexity of groups. We also obtain sequential analogs of (new) lower bounds on parametrized topological complexity of epimorphisms which are recently obtained by Espinosa Baro, Farber, Mescher and Oprea. Finally, we utilize these results to provide alternative computations for the sequential parametrized topological complexity of planar Fadell-Neuwirth fibrations.