The Borsuk-Ulam property for homotopy classes on bundles, parametrized braids groups and applications for surfaces bundles

Daciberg Lima Gonçalves, Vinicius Casteluber Laass, Weslem Liberato Silva

Let $M$ and $N$ be fiber bundles over the same base $B$, where $M$ is endowed with a free involution $\tau$ over $B$. A homotopy class $\delta \in [M,N{]}_B$ (over $B$) is said to have the…