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

Hokuto Konno; Jianfeng Lin; Anubhav Mukherjee; Juan Muñoz-Echániz

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arXiv · 2411.12202

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

Hokuto Konno·Jianfeng Lin·Anubhav Mukherjee·Juan Muñoz-Echániz

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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 $\mathbb{Z}/p$-equivariant Seiberg--Witten--Floer homology of 3-manifolds.

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Hokuto Konno, Jianfeng Lin, Anubhav Mukherjee, Juan Muñoz-Echániz. 2024-11-19. The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory. https://arxiv.org/abs/2411.12202

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