A factorization formula for the full twist of double the number of strings

We give a formula for factorizing the full twist in the braid group $\operatorname{Br}_{2m}$ in terms of four factorizations of the full twist in$\operatorname{Br}_{m}$. This formula is used to construct a symplectic 4-manifold $X$ and two regularly homotopic generic coverings $f_i\colon X\to\mathbb C\mathbb P^2$ branched along cuspidal Hurwitz curves $\overline H_i\subset\mathbb C\mathbb P^2$ (without negative nodes) having different braid monodromy factorization types. The class of fundamental groups of complements of affine plane Hurwitz curves is described in terms of generators and defining relations.