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The cobordism distance between a knot and its reverse | | Charles Livingston
; | | Date: |
24 Nov 2020 | | Abstract: | 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). | | Source: | arXiv, 2011.12287 | | Services: | Forum | Review | PDF | Favorites | |
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