2021/10/06 by Masaharu Ishikawa, Ishikawa, Masaharu, Yuya Koda +3
Mathematics · Medicine · #32S55 (Primary) 32S30 #52C35 (Secondary) #57M05 #Advanced Combinatorial Mathematics #Botulinum Toxin and Related Neurological Disorders #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2110.02431
openalex publication_date 2021/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A shadowed polyhedron is a simple polyhedron equipped with half integers on regions, called gleams, which represents a compact, oriented, smooth 4-manifold. The polyhedron is embedded in the 4-manifold and it is called a shadow of that manifold. A subpolyhedron of a shadow represents a possibly singular subsurface in the 4-manifold. In this paper, we focus on contractible shadows obtained from the unit disk by attaching annuli along generically immersed closed curves on the disk. In this case, the 4-manifold is always a 4-ball. Milnor fibers of plane curve singularities and complexified real line arrangements can be represented in this way. We give a presentation of the fundamental group of the complement of a subpolyhedron of such a shadow in the 4-ball. The method is very similar to the Wirtinger presentation of links in knot theory.