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The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory
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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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Irreducible 4-manifolds can admit exotic diffeomorphisms
The authors construct the first examples of irreducible closed 4-manifolds admitting exotic diffeomorphisms, using a families Seiberg-Witten constraint and explicit lattice automorphisms.
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