The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory

2024/11/19 by Hokuto Konno, Jianfeng Lin, Konno, Hokuto +5 · 2 citations
Mathematics · Physics and Astronomy · #32S25 #57K41 #57R58 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2411.12202

openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the monodromy diffeomorphism of a complex 2-dimensional isolated hypersurface singularity of weighted-homogeneous type has infinite order in the smooth mapping class group of the Milnor fiber, provided the singularity is not a rational double point. This is a consequence of our main result: the boundary Dehn twist diffeomorphism of an indefinite symplectic filling of the canonical contact structure on a negatively-oriented Seifert-fibered rational homology 3-sphere has infinite order in the smooth mapping class group. Our techniques make essential use of analogues of the contact invariant in the setting of ℤ/p-equivariant Seiberg--Witten--Floer homology of 3-manifolds.

Cited by

• The Boundary Dehn Twist on a Punctured Connected Sum of Two K3 Surfaces is Nontrivial in the Smooth Mapping Class Group
• Constraints on Lefschetz fibrations with four-dimensional fibers from Seiberg-Witten theory

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