Surgery on double knots and symmetries (Q578653)

This paper studies symmetries (i.e. homeomorphisms of finite order) of 3- manifolds obtained by Dehn surgeries on a double of a noninvertible knot, and shows that these manifolds admit no nontrivial symmetry except for a finite number of surgeries. Moreover, it determines when these manifolds are 2-fold branched covers of \(S^ 3\); this gives the exact range of validity of the conjecture of Whitten that ``no manifold obtained by a nontrivial surgery on a double of a noninvertible knot is a 2-fold branched covering of \(S^ 3\)''.