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 {\it Borsuk-Ulam property}.The problem is formulated in terms of an algebraic diagram, involving the 2-string braid group $B_{2}(S)$.