The unbounded difference conjecture for unknotting and slicing genus

Let KK be a knot, let us(K)u_s(K) denote its slicing number, and let gs(K)g_s(K) denote its slice genus. Unbounded difference conjecture. The difference

us(K)gs(K)u_s(K)-g_s(K)

can be arbitrarily large. This predicts that slicing number can exceed slice genus by an unbounded amount; the source gives no resolution or further context for the claim.

Sources & referencesView supporting material

Primary source

Charles Livingston, “The slicing number of a knot”, arXiv:math/0206072 (2002).

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