2024/04/06 by Cesar A. Ipanaque Zapata, Zapata, Cesar A. Ipanaque, Daciberg Lima Gonçalves +1
Mathematics · Medicine · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Neurosurgical Procedures and Complications
paper · pdf · doi:10.48550/arxiv.2404.04470
openalex publication_date 2024/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, for fibrations p:E→ B, p':E'→ B over B and a free involution τ:E→ E which satisfy the equality p∘τ=p, we discover a connection between the sectional category of the double covers q:E→ E/τ and qY:Fp'(E',2)→ Fp'(E',2)/ℤ2 from the 2-ordered fibre-wise configuration space Fp'(E',2) to its unordered quotient Fp'(E',2)/ℤ2, and the parametrized Borsuk-Ulam property (PBUP) for the triple ((p,τ);p'). Explicitly, we demonstrate that the triple ((p,τ);p') satisfies the PBUP if the sectional category of q is bigger than the sectional category of qp'. This property connects a standard problem in parametrized Borsuk-Ulam theory to current research trends in sectional category. As applictions of our results, we explore the PBUP for E, E' one of the following fibrations: trivial fibration, Hopf fibration and the Fadell-Neuwirth fibration.