Speaker:  Juan Muñoz-Echániz (Stony Brook University)

Title: Boundary Dehn twists on symplectic 4-manifold with Seifert-fibered boundary

Abstract: In this talk I will discuss the following result: the boundary Dehn twist on a symplectic filling M of a Seifert-fibered rational homology 3-sphere (negatively-oriented, equipped with its canonical contact structure) has infinite order in the smooth mapping class group of $M$ (fixing the boundary) provided $b^+ (M) > 0$. This result has applications to the monodromy of surface singularities, such as: the monodromy diffeomorphism of a weighted-homogeneous isolated hypersurface singularity of complex dimension 2 has infinite order in the smooth mapping class group of its Milnor fiber, provided the singularity is not ADE. (In turn,  the ADE singularities have finite order monodromy by Brieskorn’s Simultaneous Resolution Theorem.)

The proof involves studying the Seiberg—Witten equation in 1-parametric families of 4-manifolds, by a combination of techniques from Floer homology, symplectic and contact geometry. I will also explain how to use our techniques to obstruct boundary Dehn twists from factorising as products of Seidel—Dehn twists on Lagrangian 2-spheres and/or their squares, in both the smooth and/or symplectic mapping class groups.

This is based on joint work with Hokuto Konno, Jianfeng Lin and Anubhav Mukherjee.