2025/12/24 by Isoshima, Tsukasa, Yabuguchi, Reo
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2512.21001
Castro and Ozbagci constructed a trisection of a closed 4-manifold admitting a Lefschetz fibration with a (-1)-section such that the corresponding trisection diagram can be explicitly constructed from a monodromy of the Lefschetz fibration. In this paper, for a closed 4-manifold X admitting an achiral Lefschetz fibration with a (-n)-section, we construct a trisection of X # nℂP2 if n is positive and X # (-n)ℂP2 if n is negative such that the corresponding trisection diagram can be explicitly constructed from a monodromy of the Lefschetz fibration. We also construct a trisection of the fiber sum of two achiral Lefschetz fibrations with n- and (-n)-sections such that the corresponding trisection diagram can be explicitly constructed from monodromies of the Lefschetz fibrations.