Rational Tangle Replacement and its Consequences
June 2021
We present Montesinos and Neuwirth’s proof that 2-fold cyclic branched covers of S3 are precisely the (closed, orientable) 3-manifolds which can be obtained via surgery on a strongly-invertible link in S3. The proof uses rational tangle replacement, of which we give a short exposition. This paper was written for a course on low-dimensional topology run by Joan Licata at the ANU.