Boundary Dehn twists on Milnor fibers and Family Bauer--Furuta invariants

We proved that the boundary Dehn twist on the Milnor fiber $M_c(2,q,r)$ is an exotic diffeomorphism relative to the boundary if $q,r$ are odd, coprime integers bigger than $3$ and $(q-1)(r-1)\mathrm{/}4$ is an odd number. The proof is given by comparing the family relative Bauer–Furuta invariants of the mapping torus.