930:
968:
942:
31:
91:
211:
1009:
307:
875:
794:
341:
784:
1002:
789:
660:
193:
361:
423:
157:
188:
131:
As well as their mathematical study, wild knots have also been studied for their potential for decorative purposes in
1033:
113:
429:
493:
488:
300:
1028:
995:
183:
135:
621:
152:
946:
835:
804:
665:
56:
934:
705:
293:
742:
725:
763:
710:
324:
320:
246:
220:
860:
809:
759:
715:
675:
670:
588:
895:
720:
616:
351:
272:
230:
242:
105:
theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame.
855:
819:
754:
700:
655:
648:
538:
450:
333:
238:
98:
979:
915:
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608:
483:
475:
435:
206:
1022:
850:
638:
631:
626:
161:
865:
845:
749:
732:
528:
465:
250:
125:
548:
387:
379:
371:
975:
880:
643:
417:
397:
316:
285:
132:
51:
39:
900:
885:
840:
737:
690:
685:
680:
510:
407:
276:
234:
102:
573:
47:
967:
890:
500:
147:
117:
94:
17:
46:
if it can be "thickened", that is, if there exists an extension to an
30:
910:
558:
518:
225:
799:
97:. A knot is tame if and only if it can be represented as a finite
870:
289:
27:
Knot that can't be tied in a string of constant diameter
983:
59:
828:
772:
607:
509:
474:
332:
120:is a wild knot. It has been conjectured that every
85:
263:Browne, Cameron (December 2006), "Wild knots",
1003:
301:
8:
212:Journal of Knot Theory and Its Ramifications
209:(1994), "Quadrisecants of knots and links",
182:Voitsekhovskii, M. I. (December 13, 2014) ,
1010:
996:
308:
294:
286:
116:behavior. Every closed curve containing a
224:
77:
64:
58:
29:
174:
7:
964:
962:
941:
108:Knots that are not tame are called
25:
86:{\displaystyle S^{1}\times D^{2}}
966:
940:
929:
928:
795:DowkerâThistlethwaite notation
1:
982:. You can help Knowledge by
164:using infinite sums of knots
160:, a technique for analyzing
40:mathematical theory of knots
189:Encyclopedia of Mathematics
1050:
961:
924:
785:AlexanderâBriggs notation
277:10.1016/j.cag.2006.08.021
235:10.1142/S021821659400006X
265:Computers & Graphics
876:List of knots and links
424:KinoshitaâTerasaka knot
158:EilenbergâMazur swindle
153:Alexander horned sphere
99:closed polygonal chain
87:
35:
666:Finite type invariant
101:. In knot theory and
88:
33:
124:has infinitely many
57:
976:knot theory-related
836:Alexander's theorem
136:ornamental knotwork
83:
36:
1034:Knot theory stubs
991:
990:
956:
955:
810:Reidemeister move
676:Khovanov homology
671:Hyperbolic volume
16:(Redirected from
1041:
1012:
1005:
998:
970:
963:
944:
943:
932:
931:
896:Tait conjectures
599:
598:
584:
583:
569:
568:
461:
460:
446:
445:
430:(â2,3,7) pretzel
310:
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271:(6): 1027â1032,
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69:
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21:
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1038:
1029:Knots and links
1019:
1018:
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1016:
959:
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952:
920:
824:
790:Conway notation
774:
768:
755:Tricolorability
603:
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582:
579:
578:
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567:
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563:
562:
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484:Composite knots
470:
459:
456:
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451:Borromean rings
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207:Kuperberg, Greg
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144:
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60:
55:
54:
28:
23:
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15:
12:
11:
5:
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989:
988:
971:
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951:
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938:
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922:
921:
919:
918:
916:Surgery theory
913:
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893:
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848:
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815:Skein relation
812:
807:
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797:
792:
787:
781:
779:
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769:
767:
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760:Unknotting no.
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723:
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708:
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619:
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571:
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556:
552:
546:
542:
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532:
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522:
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513:
507:
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498:
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480:
478:
472:
471:
469:
468:
463:
457:
448:
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433:
427:
421:
415:
411:
405:
401:
395:
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385:
381:
377:
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369:
365:
359:
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349:
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338:
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329:
315:
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312:
305:
298:
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255:
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173:
172:
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162:connected sums
155:
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80:
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72:
67:
63:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1046:
1035:
1032:
1030:
1027:
1026:
1024:
1013:
1008:
1006:
1001:
999:
994:
993:
987:
985:
981:
978:article is a
977:
972:
969:
965:
960:
949:
948:
939:
937:
936:
927:
926:
923:
917:
914:
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907:
904:
902:
899:
897:
894:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
867:
864:
862:
859:
857:
854:
852:
851:Conway sphere
849:
847:
844:
842:
839:
837:
834:
833:
831:
827:
821:
818:
816:
813:
811:
808:
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803:
801:
798:
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793:
791:
788:
786:
783:
782:
780:
778:
771:
765:
761:
758:
756:
753:
751:
748:
744:
741:
740:
739:
736:
734:
731:
727:
724:
722:
719:
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714:
712:
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707:
704:
703:
702:
699:
697:
694:
692:
689:
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684:
682:
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
650:
647:
646:
645:
642:
640:
637:
633:
630:
629:
628:
625:
623:
622:Arf invariant
620:
618:
615:
614:
612:
610:
606:
590:
587:
575:
572:
560:
557:
550:
547:
540:
537:
530:
527:
520:
517:
516:
514:
512:
508:
502:
499:
495:
492:
490:
487:
486:
485:
482:
481:
479:
477:
473:
467:
464:
452:
449:
437:
434:
431:
428:
425:
422:
419:
416:
409:
406:
399:
396:
389:
386:
384:
378:
376:
370:
363:
360:
353:
350:
343:
340:
339:
337:
335:
331:
326:
322:
318:
311:
306:
304:
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297:
292:
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288:
278:
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266:
259:
256:
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208:
202:
199:
195:
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190:
185:
178:
175:
168:
163:
159:
156:
154:
151:
149:
146:
145:
141:
139:
137:
134:
129:
127:
126:quadrisecants
123:
119:
115:
112:and can have
111:
106:
104:
100:
96:
78:
74:
70:
65:
61:
53:
49:
45:
41:
32:
19:
984:expanding it
973:
958:
945:
933:
905:
861:Double torus
846:Braid theory
661:Crossing no.
656:Crosscap no.
342:Figure-eight
268:
264:
258:
226:math/9712205
216:
210:
201:
187:
177:
133:Celtic-style
130:
121:
114:pathological
109:
107:
43:
42:, a knot is
37:
696:Linking no.
617:Alternating
418:Conway knot
398:Carrick mat
352:Three-twist
317:Knot theory
184:"Wild knot"
52:solid torus
34:A wild knot
1023:Categories
856:Complement
820:Tabulation
777:operations
701:Polynomial
691:Link group
686:Knot group
649:Invertible
627:Bridge no.
609:Invariants
539:Cinquefoil
408:Perko pair
334:Hyperbolic
169:References
103:3-manifold
750:Stick no.
706:Alexander
644:Chirality
589:Solomon's
549:Septafoil
476:Satellite
436:Whitehead
362:Stevedore
219:: 41â50,
194:EMS Press
122:wild knot
93:into the
71:×
48:embedding
18:Tame knot
935:Category
805:Mutation
773:Notation
726:Kauffman
639:Brunnian
632:2-bridge
501:Knot sum
432:(12n242)
148:Wild arc
142:See also
118:wild arc
95:3-sphere
947:Commons
866:Fibered
764:problem
733:Pretzel
711:Bracket
529:Trefoil
466:L10a140
426:(11n42)
420:(11n34)
388:Endless
251:6103528
243:1265452
50:of the
38:In the
911:Writhe
881:Ribbon
716:HOMFLY
559:Unlink
519:Unknot
494:Square
489:Granny
249:
241:
974:This
901:Twist
886:Slice
841:Berge
829:Other
800:Flype
738:Prime
721:Jones
681:Genus
511:Torus
325:links
321:knots
247:S2CID
221:arXiv
980:stub
906:Wild
871:Knot
775:and
762:and
743:list
574:Hopf
323:and
110:wild
44:tame
891:Sum
412:161
410:(10
273:doi
231:doi
1025::
591:(4
576:(2
561:(0
551:(7
541:(5
531:(3
521:(0
453:(6
438:(5
402:18
400:(8
390:(7
364:(6
354:(5
344:(4
269:30
267:,
245:,
239:MR
237:,
229:,
215:,
192:,
186:,
138:.
128:.
1011:e
1004:t
997:v
986:.
600:)
596:1
585:)
581:1
570:)
566:1
555:)
553:1
545:)
543:1
535:)
533:1
525:)
523:1
462:)
458:2
447:)
443:1
414:)
404:)
394:)
392:4
382:3
380:6
374:2
372:6
368:)
366:1
358:)
356:2
348:)
346:1
327:)
319:(
309:e
302:t
295:v
275::
233::
223::
217:3
79:2
75:D
66:1
62:S
20:)
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