On the ${\mathfrak{S}}_q\overleftrightarrow{\times }{\mathfrak{S}}_q$-invariant rational cohomology of the pure braid group $P_{2q}$

Yan Fu, Gefei Wang

Let ${\mathfrak{S}}_q\overleftrightarrow{\times }{\mathfrak{S}}_q$ be the $\mathbb{Z}/2$-extension of the product of two symmetric groups ${\mathfrak{S}}_q\times {\mathfrak{S}}_q$. I…