We give a formula for the duality structure of the
–manifold
obtained by doing zero-framed surgery along a knot in the
–sphere,
starting from a diagram of the knot. We then use this to give a
combinatorial algorithm for computing the twisted Blanchfield pairing of such
–manifolds.
With the twisting defined by Casson–Gordon-style representations, we use our
computation of the twisted Blanchfield pairing to show that some subtle satellites of
genus two ribbon knots yield nonslice knots. The construction is subtle in the sense
that, once based, the infection curve lies in the second derived subgroup of the knot
group.
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