Constructing Lefschetz Fibrations with Arbitrary Slope

2025/12/03 by Tüli̇n Altunöz, Altunoz, Tulin, Adalet Çengel +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Limits and Structures in Graph Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2512.03714

openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28

Abstract

We prove that for any rational number r∈ (2,8), there exists a genus-g Lefschetz fibration over the two-sphere with large enough genus-g having the slope is r.

Citations

• Low-slope Lefschetz fibrations
• Lefschetz fibrations with arbitrary signature
• Symplectic Lefschetz fibrations with arbitrary fundamental groups

Related

• Low-slope Lefschetz fibrations
• On the Slope of Hyperelliptic Lefschetz Fibrations and the Number of Separating Vanishing Cycles
• Hyperelliptic Lefschetz fibrations and branched covering spaces
• The existence of an indecomposable minimal genus two Lefschetz fibration
• Lefschetz fibrations and Torelli groups