Diffeomorphisms of 4-manifolds from graspers

Abstract

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 ``parameterised 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 $M$.

arXiv comment29 pages, 18 figures. v2: Minor edits. v3: Major edits, improved exposition

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Cited by in corpus (1)

• On fundamental groups of spaces of framed embeddings of a circle in a 4-manifold