Dehn twist along Brieskorn spheres in their positive definite fillings

Abstract: Given any smooth 4-manifold bounding a Seifert manifold, the Seifert action on its boundary can be used to define their boundary Dehn twists. If the given 4-manifold is simply-connected, this Dehn twist is always topologically isotopic to the identity, but usually not smoothly isotopic, making it a very nice potential example of exotic diffeomorphisms. For some choices of small enough Brieskorn spheres and some choices of their fillings, it has been shown that their boundary Dehn twists are infinite-order exotic. In this talk, we prove that for any Brieskorn homology sphere bounding a positive-definite 4-manifold, their boundary Dehn twists are always infinite-order exotic, using both the equivariant Seiberg-Witten homology of Baraglia-Hekmati and the family Seiberg-Witten theory. This is a joint work with JungHwan Park and Masaki Taniguchi.