Diffeomorphisms of 4-manifolds from degree one graspers

Danica Kosanović

Published 2024-05-09, updated 2024-07-10Version 2

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