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Mathematics > Geometric Topology

arXiv:1807.01419 (math)
[Submitted on 4 Jul 2018 (v1), last revised 11 May 2020 (this version, v2)]

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

Authors:Masaharu Ishikawa, Hironobu Naoe
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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.
Comments: 17 pages, 13 figures. Some terminology is changed
Subjects: Geometric Topology (math.GT); Algebraic Geometry (math.AG)
MSC classes: 32S55 (Primary) 32S30, 57M20 (Secondary)
Cite as: arXiv:1807.01419 [math.GT]
  (or arXiv:1807.01419v2 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.1807.01419

Submission history

From: Masaharu Ishikawa [view email]
[v1] Wed, 4 Jul 2018 01:17:23 UTC (379 KB)
[v2] Mon, 11 May 2020 04:24:27 UTC (379 KB)
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