2018/07/04 by Masaharu Ishikawa, Ishikawa, Masaharu, Hironobu Naoe +1
Mathematics · #32S55 (Primary) 32S30 #57M20 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1807.01419
openalex publication_date 2018/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.