350:
277:
204:
462:
632:
115:
75:
590:
551:
507:
724:
282:
209:
410:
concordance invariants are Milnor invariants and their products, though non-finite type concordance invariants exist.
127:
739:
421:
640:
form of cobordism – it requires two submanifolds to be not just abstractly cobordant, but "cobordant in
595:
407:
80:
40:
556:
512:
360:
702:
J. Hillman, Algebraic invariants of links. Series on Knots and everything. Vol 32. World
Scientific.
399:
744:
35:
471:
720:
637:
403:
672:
Habegger, Nathan; Masbaum, Gregor (2000), "The
Kontsevich integral and Milnor's invariants",
681:
398:
of any two components of a link is one of the most elementary concordance invariants. The
717:
714:
395:
686:
733:
31:
653:
465:
122:
17:
710:
402:
is also a concordance invariant. A subtler concordance invariant are the
368:
364:
27:
Link equivalence relation weaker than isotopy but stronger than homotopy
464:. In this case one considers two submanifolds concordant if there is a
387:
A function of a link that is invariant under concordance is called a
376:
705:
Livingston, Charles, A survey of classical knot concordance, in:
418:
One can analogously define concordance for any two submanifolds
371:: isotopy implies concordance implies homotopy. A link is a
345:{\displaystyle f(L_{0}\times \{1\})=L_{1}\times \{1\}}
272:{\displaystyle f(L_{0}\times \{0\})=L_{0}\times \{0\}}
598:
559:
515:
474:
424:
285:
212:
130:
83:
43:
626:
584:
545:
501:
456:
344:
271:
198:
109:
69:
199:{\displaystyle f:L_{0}\times \to S^{n}\times }
8:
618:
612:
579:
573:
339:
333:
311:
305:
266:
260:
238:
232:
509:i.e., if there is a manifold with boundary
685:
636:This higher-dimensional concordance is a
603:
597:
564:
558:
514:
473:
442:
429:
423:
324:
296:
284:
251:
223:
211:
172:
141:
129:
101:
88:
82:
61:
48:
42:
664:
7:
457:{\displaystyle M_{0},M_{1}\subset N}
627:{\displaystyle M_{1}\times \{1\}.}
110:{\displaystyle L_{1}\subset S^{n}}
70:{\displaystyle L_{0}\subset S^{n}}
25:
585:{\displaystyle M_{0}\times \{0\}}
546:{\displaystyle W\subset N\times }
540:
528:
493:
481:
314:
289:
241:
216:
193:
181:
165:
162:
150:
1:
687:10.1016/S0040-9383(99)00041-5
553:whose boundary consists of
406:, and in fact all rational
375:if it is concordant to the
761:
502:{\displaystyle N\times ,}
707:Handbook of knot theory
628:
586:
547:
503:
458:
383:Concordance invariants
346:
273:
200:
111:
71:
629:
587:
548:
504:
459:
389:concordance invariant
347:
274:
201:
112:
72:
709:, pp 319–347,
596:
557:
513:
472:
422:
367:, and stronger than
363:. It is weaker than
361:equivalence relation
283:
210:
128:
81:
41:
713:, Amsterdam, 2005.
400:signature of a knot
121:if there exists an
624:
582:
543:
499:
454:
342:
269:
196:
107:
67:
414:Higher dimensions
404:Milnor invariants
16:(Redirected from
752:
691:
690:
689:
680:(6): 1253–1289,
669:
633:
631:
630:
625:
608:
607:
591:
589:
588:
583:
569:
568:
552:
550:
549:
544:
508:
506:
505:
500:
468:between them in
463:
461:
460:
455:
447:
446:
434:
433:
357:link concordance
351:
349:
348:
343:
329:
328:
301:
300:
278:
276:
275:
270:
256:
255:
228:
227:
205:
203:
202:
197:
177:
176:
146:
145:
116:
114:
113:
108:
106:
105:
93:
92:
76:
74:
73:
68:
66:
65:
53:
52:
21:
760:
759:
755:
754:
753:
751:
750:
749:
740:Knot invariants
730:
729:
699:
697:Further reading
694:
671:
670:
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662:
650:
599:
594:
593:
560:
555:
554:
511:
510:
470:
469:
438:
425:
420:
419:
416:
385:
355:By its nature,
320:
292:
281:
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247:
219:
208:
207:
168:
137:
126:
125:
97:
84:
79:
78:
57:
44:
39:
38:
28:
23:
22:
15:
12:
11:
5:
758:
756:
748:
747:
742:
732:
731:
728:
727:
703:
698:
695:
693:
692:
663:
661:
658:
657:
656:
649:
646:
623:
620:
617:
614:
611:
606:
602:
581:
578:
575:
572:
567:
563:
542:
539:
536:
533:
530:
527:
524:
521:
518:
498:
495:
492:
489:
486:
483:
480:
477:
453:
450:
445:
441:
437:
432:
428:
415:
412:
396:linking number
384:
381:
341:
338:
335:
332:
327:
323:
319:
316:
313:
310:
307:
304:
299:
295:
291:
288:
268:
265:
262:
259:
254:
250:
246:
243:
240:
237:
234:
231:
226:
222:
218:
215:
195:
192:
189:
186:
183:
180:
175:
171:
167:
164:
161:
158:
155:
152:
149:
144:
140:
136:
133:
104:
100:
96:
91:
87:
64:
60:
56:
51:
47:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
757:
746:
743:
741:
738:
737:
735:
726:
725:0-444-51452-X
722:
719:
716:
712:
708:
704:
701:
700:
696:
688:
683:
679:
675:
668:
665:
659:
655:
652:
651:
647:
645:
643:
639:
634:
621:
615:
609:
604:
600:
576:
570:
565:
561:
537:
534:
531:
525:
522:
519:
516:
496:
490:
487:
484:
478:
475:
467:
451:
448:
443:
439:
435:
430:
426:
413:
411:
409:
405:
401:
397:
392:
390:
382:
380:
378:
374:
370:
366:
362:
358:
353:
336:
330:
325:
321:
317:
308:
302:
297:
293:
286:
263:
257:
252:
248:
244:
235:
229:
224:
220:
213:
190:
187:
184:
178:
173:
169:
159:
156:
153:
147:
142:
138:
134:
131:
124:
120:
102:
98:
94:
89:
85:
62:
58:
54:
49:
45:
37:
33:
19:
706:
677:
673:
667:
641:
635:
417:
393:
388:
386:
372:
356:
354:
118:
29:
408:finite type
32:mathematics
734:Categories
660:References
654:Slice knot
373:slice link
206:such that
119:concordant
18:Slice link
745:Manifolds
610:×
571:×
526:×
520:⊂
479:×
466:cobordism
449:⊂
331:×
303:×
258:×
230:×
179:×
166:→
148:×
123:embedding
95:⊂
55:⊂
711:Elsevier
674:Topology
648:See also
638:relative
369:homotopy
718:2179265
365:isotopy
723:
377:unlink
359:is an
34:, two
36:links
721:ISBN
592:and
394:The
279:and
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