Kulikov, Vik. S. A full-twist factorization formula with a double number of strings. (English. Russian original) Zbl 1064.57027 Izv. Math. 68, No. 1, 125-158 (2004); translation from Izv. Ross. Akad. Nauk Ser. Mat. 68, No. 1, 123-158 (2004). Summary: We give a formula for factorizing the full twist in the braid group \(\text{Br}_{2m}\) in terms of four factorizations of the full twist in \(\text{Br}_m\). This formula is used to construct a symplectic 4-manifold \(X\) and two regularly homotopic generic coverings \(f_i:X\to\mathbb{C}\mathbb{P}^2\) 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. Cited in 1 Document MSC: 57Q45 Knots and links in high dimensions (PL-topology) (MSC2010) 57M05 Fundamental group, presentations, free differential calculus 20F36 Braid groups; Artin groups Keywords:full twist; braid group; symplectic manifold; generic coverings; cuspidal Hurwitz curves; fundamental groups PDFBibTeX XMLCite \textit{Vik. S. Kulikov}, Izv. Math. 68, No. 1, 125--158 (2004; Zbl 1064.57027); translation from Izv. Ross. Akad. Nauk Ser. Mat. 68, No. 1, 123--158 (2004) Full Text: DOI arXiv