Braided surfaces and their characteristic maps

(joint work with P. Pagotto) We show that branched coverings of surfaces of large enough genus arise as characteristic maps of braided surfaces, i.e. can be lifted to embeddings into 4-dimensional thickenings (2-prems).
In the reverse direction we show that any nonabelian surface group has infinitely many finite simple nonabelian groups quotients with characteristic kernels which do not contain any simple loops and hence the quotient maps do not factor through free groups.
By a pullback construction, finite dimensional Hermitian representations of braid groups provide invariants for the braided surfaces. We show that the strong equivalence classes of braided surfaces are separated by such invariants if and only if they are profinitely separated.

Connect to Zoom: https://zoom.us/j/97302991744
Access code: the Euler characteristic of the wedge of two circles
(the password is not the specified phrase but the number that it determines)