The Conway knot is topologically slice

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conway_knot_topologically_slice

Submitter: Kim Morrison.

Notes: Freedman's theorem applied to the Conway knot 11n34, whose Alexander polynomial is trivial. The proof requires Freedman's full topological surgery machinery in dimension four; this is genuinely hard. Pairs with `conway_knot_not_smoothly_slice` (Piccirillo) to give the celebrated smooth/topological dichotomy for a specific named knot.

Source: Freedman, *The topology of four-dimensional manifolds*, J. Diff. Geom. 17 (1982). See also Freedman-Quinn, *Topology of 4-Manifolds*, Princeton 1990.

Informal solution: Compute the Alexander polynomial of the Conway knot from a Seifert matrix and verify Delta(t) = 1. Apply Freedman's theorem: every knot in S^3 with Alexander polynomial 1 bounds a locally flat topological disk in B^4. Construct the resulting locally flat disk image inside R^3 x [0, infty) and verify the local flatness condition pointwise.

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