= Robion Kirby
{c}
<Robion Kirby> developed tools for low-dimensional <topology>, including <Kirby calculus>. His 1978 paper describes three-manifolds by surgery on framed links in the three-sphere.<A calculus for framed links in S3 by Robion Kirby>[Original byline and section 1]{ref}
Different link diagrams can describe the same manifold. Kirby's theorem identifies moves—handle slides and the addition or removal of an isolated appropriately framed unknot—that relate such descriptions. This turns an equivalence problem about manifolds into controlled operations on diagrams, while also connecting the diagrams to four-dimensional handle attachments.<A calculus for framed links in S3 by Robion Kirby>[Operations One and Two and Theorem 1, pp. 35–36]{ref}
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