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math.GT2020
The cobordism distance between a knot and its reverse
Charles Livingston
The cobordism distance between knots, d(K,J), equals the four-genus g_4(K # -J). We consider d(K,K^r), where K^r is the reverse of K. It is elementary that 0 \le d(K,K^r) \le 2g_4(…
math.GT2020
Unknotting with a single twist
Samantha Allen, Charles Livingston
Given a knot in the three-sphere, is it possible to unknot it by performing a single twist, and if so, what are the possible linking numbers of such a twist? We develop obstruction…