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Keywords:
continued fraction; Hopf link; lens space; rational surgery; Rolfsen moves
continued fraction; Hopf link; lens space; rational surgery; Rolfsen moves
Summary:
It is clear that every rational surgery on a Hopf link in $3$-sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a corollary, we recover the (well-known) result on the criterion for when rational surgery on a Hopf link gives the $3$-sphere.
References:
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