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

机译:字符串数量加倍的完全分解的分解公式

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摘要

We give a formula for factorizing the full twist in the braid group Br2m in terms of four factorizations of the full twist in Brm. This formula is used to construct a symplectic 4-manifold X and two regularly homotopic generic coverings f_i: X →CP~2 branched along cuspidal Hurwitz curves H-bar_i is contained in CP~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.
机译:我们给出了一个公式,用于将编织组Br2m中的全捻分解为Brm中全捻的四个分解。该公式用于构造辛4流形X和两个规则的同构通用覆盖f_i:X→CP〜2沿着尖齿Hurwitz曲线分支H-bar_i包含在CP〜2中(无负节点),具有不同的辫子单峰分解因子类型。仿射平面Hurwitz曲线的补码的基本组类别按照生成器和定义关系来描述。

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