Diffeomorphisms of 4‐manifolds from graspers

We relate degree one grasper families of embedded circles to various constructions of diffeomorphisms found in the literature, theta clasper classes of Watanabe, barbell diffeomorphisms of Budney and Gabai, and twin twists of Gay and Hartman. We use a ‘parametrised surgery map’ that for a smooth 4-manifold 𝑀 takes loops of framed embeddings of 𝑆 1 in the manifold obtained by surgery on some 2-sphere in 𝑀, to the mapping class group of 𝑀.