English

Full twists factorization formula for double number of strings

Algebraic Geometry 2007-05-23 v1 Symplectic Geometry

Abstract

A formula for factorizations of the full twist in the braid group Br2mBr_{2m} depending on any four factorizations of the full twist in BrmBr_{m} is given. Applying this formula, a symplectic 4-manifold XX and two isotopic generic coverings fi:XCP2f_i :X\to \mathbb C\mathbb P^2, branched, respectively, along cuspidal Hurwitz curves HˉiCP2\bar H_i\subset \mathbb C\mathbb P^2 (without negative nodes) having different braid monodromy factorization types, are constructed. The class of the fundamental groups of the complements of the affine plane Hurwitz curves is described in terms of generators and defining relations.

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Cite

@article{arxiv.math/0308178,
  title  = {Full twists factorization formula for double number of strings},
  author = {Vik. S. Kulikov},
  journal= {arXiv preprint arXiv:math/0308178},
  year   = {2007}
}

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39 pages