English

Milnor fibration, A'Campo's divide and Turaev's shadow

Geometric Topology 2020-05-12 v2 Algebraic Geometry

Abstract

We give a method for constructing a shadowed polyhedron from a divide. The 4-manifold reconstructed from a shadowed polyhedron admits the structure of a Lefschetz fibration if it satisfies a certain property, which we call the LF-property. We will show that the shadowed polyhedron constructed from a divide satisfies this property and the Lefschetz fibration of this polyhedron is isomorphic to the Lefschetz fibration of the divide. Furthermore, applying the same technique to certain free divides we will show that the links of those free divides are fibered with positive monodromy.

Keywords

Cite

@article{arxiv.1807.01419,
  title  = {Milnor fibration, A'Campo's divide and Turaev's shadow},
  author = {Masaharu Ishikawa and Hironobu Naoe},
  journal= {arXiv preprint arXiv:1807.01419},
  year   = {2020}
}

Comments

17 pages, 13 figures. Some terminology is changed