Duncan McCoy

On 2-bridge knots with differing smooth and topological slice genera

We give infinitely many examples of 2-bridge knots for which the topological and smooth slice genera differ. The smallest of these is the 12-crossing knot

Non-integer surgery and branched double covers of alternating knots

12a255

On Calculating the Slice Genera of 11- and 12-Crossing Knots

. These also provide the first known examples of alternating knots for which the smooth and topological genera differ.

Bounds on alternating surgery slopes

We show that if the branched double cover of an alternating link arises as

Alternating knots with unknotting number one

p/q \in \mathbb{Q} \setminus \mathbb{Z}

A note on the smooth and topological slice genera of 2-bridge knots

surgery on a knot in

Surgeries, sharp 4-manifolds and the Alexander polynomial

S^3

A note on calculating the slice genus of 11- and 12-crossing knots

, then this is exhibited by a rational tangle replacement in an alternating diagram.

Bounds on surgeries branching over alternating knots

ABSTRACT This article contains the results of efforts to determine the values of the smooth and the topological slice genus of 11- and 12-crossing knots. Upper bounds for these genera were produced by using a computer to search for genus one concordances between knots. For the topological slice genus, further upper bounds were produced using the algebraic genus. Lower bounds were obtained using a new obstruction from the Seifert form and by the use of Donaldson’s diagonalization theorem. These results complete the computation of the topological slice genera for all knots with at most 11 crossings and leaves the smooth genera unknown for only two 11-crossing knots. For 12 crossings, there remain merely 25 knots whose smooth or topological slice genus is unknown.

On the characterising slopes of hyperbolic knots

We show that if