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Infinite order of boundary Dehn twists for all Seifert-fibered fillings

Prove that for any negatively oriented Seifert-fibered 3-manifold Y and any compact symplectic filling (M, ω) of a contact structure ξ on Y with b+(M) > 0, the boundary Dehn twist τM has infinite order in the smooth mapping class group π0(Diff(M, ∂)), without assuming ξ is S1-invariant.

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Background

The main theorem of the paper establishes that when Y is a negatively oriented Seifert-fibered rational homology sphere and ξ is an S1-invariant contact structure, any symplectic filling (M, ω) with b+(M)>0 has boundary Dehn twist τM of infinite order in π0(Diff(M, ∂)).

The authors expect the S1-invariance hypothesis on the contact structure can be removed and conjecture the result holds for any contact structure ξ on Y, provided (M, ω) is a symplectic filling with b+(M)>0.

References

Conjecture Let $Y$ be a negatively-oriented Seifert-fibered 3-manifold, and let $(M,\omega )$ be a compact symplectic filling of $(Y,\xi)$ with $b{+}(M)>0$ (where $\xi$ is a contact structure on $Y$). Then the boundary Dehn twist $\tau_{M}$ has infinite order in $\pi_0 ( \mathrm{Diff}(M, \partial ) )$.

— The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory (2411.12202 - Konno et al., 19 Nov 2024) in Conjecture, Introduction, Subsection 1.2 (Boundary Dehn twists on indefinite symplectic fillings)