2019/12/12 by Daciberg Lima Gonçalves, Gonçalves, Daciberg Lima, John Guaschi +3
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.1912.06017
openalex publication_date 2019/12/12 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28
Let M be a topological space that admits a free involution τ, and let N be a topological space. A homotopy class β∈ [ M,N ] is said to have \it the Borsuk-Ulam property with respect to τ if for every representative map f: M → N of β, there exists a point x ∈ M such that f(τ(x))= f(x). In this paper, we determine the homotopy classes of maps from the 2-torus T2 to the Klein bottle K2 that possess the Borsuk-Ulam property with respect to a free involution τ1 of T2 for which the orbit space is T2. Our results are given in terms of a certain family of homomorphisms involving the fundamental groups of T2 and K2.