论文标题
结与反向之间的恢复距离
The cobordism distance between a knot and its reverse
论文作者
论文摘要
D（K，J）之间的COBORDISM距离等于四生G_4（K＃-J）。我们考虑d（k，k^r），其中k^r是k的相反。这里表明，对于G_4（k）= g_3（k）的任何结（例如，具有G_3（k）= 1的非裂缝结或非常明显的准阳性结），一个人的D（k，k^r）严格少于两次G_4（k）。结果表明，对于任意正g，存在d（k，k^r）= g = g_4（k）的结。尚无d（k，k^r）> g_4（k）的已知示例。
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(K) and it is known that there are knots K for which d(K,K^r) is arbitrarily large. Here it is shown that for any knot for which g_4(K) = g_3(K) (such as non-slice knots with g_3(K) = 1 or strongly quasi-positive knots), one has that d(K,K^r) is strictly less that twice g_4(K). It is shown that for arbitrary positive g, there exist knots for which d(K,K^r) = g = g_4(K). There are no known examples for which d(K,K^r) > g_4(K).
