Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cobordism distance between a knot and its reverse   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).

16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess