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Mathematics > Geometric Topology

arXiv:2411.12202 (math)
[Submitted on 19 Nov 2024]

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

Authors: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.
Comments: Comments welcome!
Subjects: Geometric Topology (math.GT); Algebraic Geometry (math.AG); Symplectic Geometry (math.SG)
MSC classes: 57K41, 57R58, 32S25
Cite as: arXiv:2411.12202 [math.GT]
  (or arXiv:2411.12202v1 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.2411.12202

Submission history

From: Juan Muñoz-Echániz [view email]
[v1] Tue, 19 Nov 2024 03:40:37 UTC (36 KB)
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