This page gives the current results of a search for knots from the standard tables which can be built by the construction found in the paper "Persistent laminations from Seifert surfaces". Currently just over 45 percent (i.e., 116) of the (250) prime knots with ten or fewer crossings can be so constructed. You can download a zip file containing illustrative projections of these knots, in a form readable by SnapPea. How to read this table:
Knots that are in bold red can be
built by the construction. Knots in italic
green cannot be built (they are torus knots). The knots
in |
3_1 | 5_1 | |||||||||
6_1 | 7_1 | |||||||||
8_1 | 8_3 | 8_6 | 8_7 | 8_8 | 8_9 | 8_10 | ||||
8_11 | 8_13 | 8_14 | 8_16 | 8_19 | 8_20 | |||||
9_1 | 9_7 | 9_8 | ||||||||
9_12 | 9_14 | 9_19 | ||||||||
9_21 | 9_24 | 9_25 | 9_26 | 9_27 | ||||||
9_32 | 9_36 | 9_37 | 9_39 | |||||||
9_42 | 9_43 | 9_44 | 9_46 | 9_47 | 9_48 | |||||
10_1 | 10_3 | 10_4 | 10_5 | 10_6 | 10_7 | 10_8 | 10_9 | 10_10 | ||
10_11 | 10_12 | 10_13 | 10_16 | 10_17 | 10_18 | 10_20 | ||||
10_21 | 10_22 | 10_23 | 10_24 | 10_26 | 10_27 | 10_29 | 10_30 | |||
10_35 | 10_36 | 10_38 | ||||||||
10_43 | 10_47 | 10_48 | 10_50 | |||||||
10_53 | 10_55 | 10_56 | 10_58 | |||||||
10_62 | 10_63 | 10_64 | 10_65 | 10_67 | 10_68 | |||||
10_74 | 10_77 | 10_79 | 10_80 | |||||||
10_82 | 10_83 | 10_86 | 10_87 | 10_90 | ||||||
10_91 | 10_94 | 10_97 | 10_98 | 10_99 | ||||||
10_102 | 10_104 | 10_106 | 10_109 | 10_110 | ||||||
10_111 | ||||||||||
10_122 | 10_124 | 10_125 | 10_126 | 10_127 | ||||||
10_133 | 10_134 | 10_136 | 10_137 | 10_140 | ||||||
10_141 | 10_143 | 10_144 | 10_146 | 10_147 | 10_148 | 10_150 | ||||
10_152 | 10_153 | 10_154 | 10_158 | 10_159 | ||||||
10_163 | 10_165 |