Non-integer surgery and branched double covers of alternating knots

Abstract

We show that if the branched double cover of an alternating link arises as $p/q\in \mathbb{Q}\setminus \mathbb{Z}$ surgery on a knot in $S^3$, then this is exhibited by a rational tangle replacement in an alternating diagram.

27 pages, 10 figures

References in corpus (1)

• Deficiency Symmetries of Surgeries in $S^3$

Cited by in corpus (6)

• Mapping cone formula in Heegaard Floer homology and Dehn surgery on knots in $S^3$
• Surgeries, sharp 4-manifolds and the Alexander polynomial
• Bounds on alternating surgery slopes
• Khovanov homology and rational unknotting
• Alternating Surgeries
• The realization problem for non-integer Seifert fibered surgeries