1145:
1157:
26:
99:
110:
476:
389:
272:
1218:
1188:
522:
439:
1090:
326:
1193:
1009:
1198:
414:
186:, and showed that the knot is not a smoothly slice knot, though it is topologically slice (the Kinoshita–Terasaka knot is both).
1213:
556:
1208:
1203:
999:
1004:
875:
53:
576:
638:
152:
1223:
644:
708:
703:
515:
265:
836:
1161:
1050:
1019:
490:
479:
148:
103:
880:
63:
1183:
1149:
920:
508:
164:
160:
957:
940:
978:
925:
539:
535:
370:
141:
137:
315:
1075:
1024:
974:
930:
890:
885:
803:
183:
43:
390:"A math problem stumped experts for 50 years. This grad student from Maine solved it in days"
1110:
935:
831:
566:
362:
244:
156:
374:
1070:
1034:
969:
915:
870:
863:
753:
665:
548:
494:
483:
179:
78:
290:
1130:
1029:
991:
910:
823:
698:
690:
650:
470:
249:
232:
1177:
1065:
853:
846:
841:
1080:
1060:
964:
947:
743:
680:
182:, 50 years after John Horton Conway first proposed the knot. Her proof made use of
33:
763:
602:
594:
586:
207:
1095:
858:
612:
531:
500:
366:
125:
121:
90:
1115:
1100:
1055:
952:
905:
900:
895:
725:
622:
175:
86:
82:
1120:
788:
1105:
715:
109:
25:
1125:
773:
733:
440:"In a Single Measure, Invariants Capture the Essence of Math Objects"
168:
98:
1014:
108:
97:
1085:
504:
487:
159:. Both knots also have the curious property of having the same
466:
415:"Graduate Student Solves Decades-Old Conway Knot Problem"
353:
Piccirillo, Lisa (2020). "The Conway knot is not slice".
1043:
987:
822:
724:
689:
547:
72:
62:
52:
42:
32:
18:
233:"Homomorphisms of Knot Groups on Finite Groups"
516:
8:
348:
346:
201:
199:
178:of the Conway knot was resolved in 2020 by
523:
509:
501:
316:"Knot theory and the Alexander polynomial"
24:
248:
195:
117:Prime knot named for John Horton Conway
102:Conway knot emblem on a closed gate at
15:
7:
1156:
14:
314:Litjens, Bart (August 16, 2011).
250:10.1090/S0025-5718-1971-0295332-4
1219:Non-tricolorable knots and links
1155:
1144:
1143:
278:from the original on 2016-12-16.
155:, with which it shares the same
1189:Non-alternating knots and links
332:from the original on 2020-06-09
140:with 11 crossings, named after
1010:Dowker–Thistlethwaite notation
1:
375:10.4007/annals.2020.191.2.5
367:10.4007/annals.2020.191.2.5
1240:
1194:Hyperbolic knots and links
237:Mathematics of Computation
1199:Unfibered knots and links
1139:
1000:Alexander–Briggs notation
77:
23:
264:Chmutov, Sergei (2007).
87:slice (topological only)
1091:List of knots and links
639:Kinoshita–Terasaka knot
184:Rasmussen's s-invariant
153:Kinoshita–Terasaka knot
1214:Chiral knots and links
295:homepages.math.uic.edu
231:Riley, Robert (1971).
114:
106:
104:Isaac Newton Institute
1209:Slice knots and links
1204:Prime knots and links
881:Finite type invariant
394:Boston Globe Magazine
355:Annals of Mathematics
212:mathworld.wolfram.com
112:
101:
161:Alexander polynomial
1051:Alexander's theorem
289:Kauffman, Louis H.
206:Weisstein, Eric W.
124:, in particular in
1224:John Horton Conway
493:2020-06-27 at the
482:2020-06-27 at the
438:Klarreich, Erica.
413:Klarreich, Erica.
142:John Horton Conway
136:) is a particular
115:
107:
1171:
1170:
1025:Reidemeister move
891:Khovanov homology
886:Hyperbolic volume
174:The issue of the
165:Conway polynomial
147:It is related by
96:
95:
44:Hyperbolic volume
1231:
1159:
1158:
1147:
1146:
1111:Tait conjectures
814:
813:
799:
798:
784:
783:
676:
675:
661:
660:
645:(−2,3,7) pretzel
525:
518:
511:
502:
454:
453:
451:
450:
435:
429:
428:
426:
425:
410:
404:
403:
401:
400:
385:
379:
378:
350:
341:
340:
338:
337:
331:
320:
311:
305:
304:
302:
301:
286:
280:
279:
277:
270:
261:
255:
254:
252:
243:(115): 603–619.
228:
222:
221:
219:
218:
203:
157:Jones polynomial
28:
16:
1239:
1238:
1234:
1233:
1232:
1230:
1229:
1228:
1174:
1173:
1172:
1167:
1135:
1039:
1005:Conway notation
989:
983:
970:Tricolorability
818:
812:
809:
808:
807:
797:
794:
793:
792:
782:
779:
778:
777:
769:
759:
749:
739:
720:
699:Composite knots
685:
674:
671:
670:
669:
666:Borromean rings
659:
656:
655:
654:
628:
618:
608:
598:
590:
582:
572:
562:
543:
529:
495:Wayback Machine
486:illustrated by
484:Wayback Machine
463:
458:
457:
448:
446:
444:Quanta Magazine
437:
436:
432:
423:
421:
419:Quanta Magazine
412:
411:
407:
398:
396:
388:Wolfson, John.
387:
386:
382:
352:
351:
344:
335:
333:
329:
323:esc.fnwi.uva.nl
318:
313:
312:
308:
299:
297:
288:
287:
283:
275:
268:
263:
262:
258:
230:
229:
225:
216:
214:
208:"Conway's Knot"
205:
204:
197:
192:
180:Lisa Piccirillo
118:
54:Conway notation
12:
11:
5:
1237:
1235:
1227:
1226:
1221:
1216:
1211:
1206:
1201:
1196:
1191:
1186:
1176:
1175:
1169:
1168:
1166:
1165:
1153:
1140:
1137:
1136:
1134:
1133:
1131:Surgery theory
1128:
1123:
1118:
1113:
1108:
1103:
1098:
1093:
1088:
1083:
1078:
1073:
1068:
1063:
1058:
1053:
1047:
1045:
1041:
1040:
1038:
1037:
1032:
1030:Skein relation
1027:
1022:
1017:
1012:
1007:
1002:
996:
994:
985:
984:
982:
981:
975:Unknotting no.
972:
967:
962:
961:
960:
950:
945:
944:
943:
938:
933:
928:
923:
913:
908:
903:
898:
893:
888:
883:
878:
873:
868:
867:
866:
856:
851:
850:
849:
839:
834:
828:
826:
820:
819:
817:
816:
810:
801:
795:
786:
780:
771:
767:
761:
757:
751:
747:
741:
737:
730:
728:
722:
721:
719:
718:
713:
712:
711:
706:
695:
693:
687:
686:
684:
683:
678:
672:
663:
657:
648:
642:
636:
630:
626:
620:
616:
610:
606:
600:
596:
592:
588:
584:
580:
574:
570:
564:
560:
553:
551:
545:
544:
530:
528:
527:
520:
513:
505:
499:
498:
474:
471:The Knot Atlas
462:
461:External links
459:
456:
455:
430:
405:
380:
361:(2): 581–591.
342:
325:. p. 12.
306:
281:
266:"Mutant Knots"
256:
223:
194:
193:
191:
188:
116:
94:
93:
75:
74:
70:
69:
66:
64:Thistlethwaite
60:
59:
56:
50:
49:
46:
40:
39:
36:
30:
29:
21:
20:
13:
10:
9:
6:
4:
3:
2:
1236:
1225:
1222:
1220:
1217:
1215:
1212:
1210:
1207:
1205:
1202:
1200:
1197:
1195:
1192:
1190:
1187:
1185:
1182:
1181:
1179:
1164:
1163:
1154:
1152:
1151:
1142:
1141:
1138:
1132:
1129:
1127:
1124:
1122:
1119:
1117:
1114:
1112:
1109:
1107:
1104:
1102:
1099:
1097:
1094:
1092:
1089:
1087:
1084:
1082:
1079:
1077:
1074:
1072:
1069:
1067:
1066:Conway sphere
1064:
1062:
1059:
1057:
1054:
1052:
1049:
1048:
1046:
1042:
1036:
1033:
1031:
1028:
1026:
1023:
1021:
1018:
1016:
1013:
1011:
1008:
1006:
1003:
1001:
998:
997:
995:
993:
986:
980:
976:
973:
971:
968:
966:
963:
959:
956:
955:
954:
951:
949:
946:
942:
939:
937:
934:
932:
929:
927:
924:
922:
919:
918:
917:
914:
912:
909:
907:
904:
902:
899:
897:
894:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
865:
862:
861:
860:
857:
855:
852:
848:
845:
844:
843:
840:
838:
837:Arf invariant
835:
833:
830:
829:
827:
825:
821:
805:
802:
790:
787:
775:
772:
765:
762:
755:
752:
745:
742:
735:
732:
731:
729:
727:
723:
717:
714:
710:
707:
705:
702:
701:
700:
697:
696:
694:
692:
688:
682:
679:
667:
664:
652:
649:
646:
643:
640:
637:
634:
631:
624:
621:
614:
611:
604:
601:
599:
593:
591:
585:
578:
575:
568:
565:
558:
555:
554:
552:
550:
546:
541:
537:
533:
526:
521:
519:
514:
512:
507:
506:
503:
496:
492:
489:
485:
481:
478:
475:
472:
468:
465:
464:
460:
445:
441:
434:
431:
420:
416:
409:
406:
395:
391:
384:
381:
376:
372:
368:
364:
360:
356:
349:
347:
343:
328:
324:
317:
310:
307:
296:
292:
285:
282:
274:
267:
260:
257:
251:
246:
242:
238:
234:
227:
224:
213:
209:
202:
200:
196:
189:
187:
185:
181:
177:
172:
170:
166:
162:
158:
154:
150:
145:
143:
139:
135:
134:Conway's knot
131:
127:
123:
111:
105:
100:
92:
88:
84:
80:
76:
71:
67:
65:
61:
57:
55:
51:
47:
45:
41:
37:
35:
31:
27:
22:
17:
1160:
1148:
1076:Double torus
1061:Braid theory
876:Crossing no.
871:Crosscap no.
632:
557:Figure-eight
447:. Retrieved
443:
433:
422:. Retrieved
418:
408:
397:. Retrieved
393:
383:
358:
354:
334:. Retrieved
322:
309:
298:. Retrieved
294:
284:
259:
240:
236:
226:
215:. Retrieved
211:
173:
146:
133:
129:
119:
1184:Knot theory
911:Linking no.
832:Alternating
633:Conway knot
613:Carrick mat
567:Three-twist
532:Knot theory
477:Conway knot
467:Conway knot
130:Conway knot
126:knot theory
122:mathematics
113:Conway knot
19:Conway knot
1178:Categories
1071:Complement
1035:Tabulation
992:operations
916:Polynomial
906:Link group
901:Knot group
864:Invertible
842:Bridge no.
824:Invariants
754:Cinquefoil
623:Perko pair
549:Hyperbolic
449:2020-06-08
424:2020-05-19
399:2020-08-24
336:2020-06-09
300:2020-06-09
217:2020-05-19
190:References
79:hyperbolic
965:Stick no.
921:Alexander
859:Chirality
804:Solomon's
764:Septafoil
691:Satellite
651:Whitehead
577:Stevedore
176:sliceness
58:.−(3,2).2
34:Braid no.
1150:Category
1020:Mutation
988:Notation
941:Kauffman
854:Brunnian
847:2-bridge
716:Knot sum
647:(12n242)
491:Archived
488:knotilus
480:Archived
327:Archived
273:Archived
149:mutation
1162:Commons
1081:Fibered
979:problem
948:Pretzel
926:Bracket
744:Trefoil
681:L10a140
641:(11n42)
635:(11n34)
603:Endless
291:"KNOTS"
167:as the
151:to the
48:11.2191
1126:Writhe
1096:Ribbon
931:HOMFLY
774:Unlink
734:Unknot
709:Square
704:Granny
373:
169:unknot
128:, the
91:chiral
89:,
85:,
81:,
1116:Twist
1101:Slice
1056:Berge
1044:Other
1015:Flype
953:Prime
936:Jones
896:Genus
726:Torus
540:links
536:knots
371:JSTOR
330:(PDF)
319:(PDF)
276:(PDF)
269:(PDF)
83:prime
73:Other
68:11n34
1121:Wild
1086:Knot
990:and
977:and
958:list
789:Hopf
538:and
163:and
138:knot
132:(or
1106:Sum
627:161
625:(10
469:on
363:doi
359:191
245:doi
120:In
1180::
806:(4
791:(2
776:(0
766:(7
756:(5
746:(3
736:(0
668:(6
653:(5
617:18
615:(8
605:(7
579:(6
569:(5
559:(4
442:.
417:.
392:.
369:.
357:.
345:^
321:.
293:.
271:.
241:25
239:.
235:.
210:.
198:^
171:.
144:.
815:)
811:1
800:)
796:1
785:)
781:1
770:)
768:1
760:)
758:1
750:)
748:1
740:)
738:1
677:)
673:2
662:)
658:1
629:)
619:)
609:)
607:4
597:3
595:6
589:2
587:6
583:)
581:1
573:)
571:2
563:)
561:1
542:)
534:(
524:e
517:t
510:v
497:.
473:.
452:.
427:.
402:.
377:.
365::
339:.
303:.
253:.
247::
220:.
38:3
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
