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.[ref]
A calculus for framed links in S3 by Robion Kirby. Original byline and section 1
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.[ref]
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Robion Kirby is a prominent American mathematician known for his work in the field of topology, particularly in low-dimensional topology and knot theory. He has made significant contributions to our understanding of 3-manifolds and has been involved in developing techniques for studying and classifying these mathematical objects. Kirby is perhaps best known for the "Kirby diagram," which is a way to represent a 4-manifold using embedded disks in a 3-manifold.