On Torelli groups and Dehn twists of smooth 4‐manifolds

Abstract This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of . Secondly, we give an alternative proof of a consequence of work of Saeki, namely that the Dehn twist along the boundary sphere of a simply connected closed smooth 4‐manifold with is trivial after taking connected sums with enough copies of .