The Borsuk-Ulam property for maps from the product of two surfaces into a surface - Gonçalves, Daciberg Lima; dos Santos, Anderson Paião; Silva, Weslem Liberato (Topological Methods in Nonlinear Analysis, 2021)
Let X, Y, S be closed connected surfaces and τ × β a diagonal involution on X × Y where τ and β are free involutions on X and Y, respectively. In this work we study when the triple (X × Y, τ × β, S) satisfies the Borsuk-Ulam property. The problem is formulated in terms of an algebraic diagram, involving the 2-string braid group B_2(S).