Geodesic
A~factorization formula for the full twist of double the number of strings
Izvestiya. Mathematics , Tome 68 (2004) no. 1, pp. 125-158

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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. 
@article{IM2_2004_68_1_a4,
     author = {Vik. S. Kulikov},
     title = {A~factorization formula for the full twist of double the number of strings},
     journal = {Izvestiya. Mathematics },
     pages = {125--158},
     publisher = {mathdoc},
     volume = {68},
     number = {1},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_1_a4/}
}
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Vik. S. Kulikov. A~factorization formula for the full twist of double the number of strings. Izvestiya. Mathematics , Tome 68 (2004) no. 1, pp. 125-158. http://geodesic.mathdoc.fr/item/IM2_2004_68_1_a4/