Abstract：

Given a 4-manifold X bounded by a Seifert manifold, one can use the circle action on the boundary to define a diffeomorphism on X, called the boundary Dehn twist. Such boundary Dehn twist naturally arises from singularity theory. A recent result by Konno-Mallick-Taniguchi shows that when X is a certain Milnor fiber, this boundary Dehn twist is topologically isotopic to the identity but not smoothly so. In this talk, we will discuss an approach to generalize this result using monopole Floer homology. Motivation from algebraic geometry will also be discussed. This talk is based on a joint work in progress with Hokuto Konno, Anubhav Mukherjee and Juan Munoz-Echaniz.