2025/12/06 by Tanaka, Atsushi
Engineering · Mathematics · #57K10 #57K40 #57K41 #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · doi:10.48550/arxiv.2512.06302
openalex publication_date 2025/12/06 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
Loi-Piergallini, Akbulut-Ozbagci, and Akbulut-Arikan showed that every compact Stein surface admits a positive allowable Lefschetz fibration over the disk D2 with bounded fibers (PALF in short), and they provided constructions of PALF's corresponding to compact Stein surfaces. In this paper, we present a simple method for constructing a PALF from a 2-handlebody decomposition of any given compact Stein surface. Our method yields PALF's whose regular fibers have small genus, and it provides an alternative constructive proof of the above result. We also define the minimal genus of a regular fiber of a PALF on the knot trace of a knot K with framing one less than its maximal Thurston-Bennequin number as an invariant of K. When the grid number of K is N, our construction produces a PALF whose regular fiber has genus at most (N - 1)/2, showing that the defined invariant is bounded above by (N - 1)/2.