339:
266:
193:
451:
621:
104:
64:
579:
540:
496:
713:
271:
198:
399:
concordance invariants are Milnor invariants and their products, though non-finite type concordance invariants exist.
116:
728:
410:
629:
form of cobordism – it requires two submanifolds to be not just abstractly cobordant, but "cobordant in
584:
396:
69:
29:
545:
501:
349:
691:
J. Hillman, Algebraic invariants of links. Series on Knots and everything. Vol 32. World
Scientific.
388:
733:
24:
460:
709:
626:
392:
661:
Habegger, Nathan; Masbaum, Gregor (2000), "The
Kontsevich integral and Milnor's invariants",
670:
387:
of any two components of a link is one of the most elementary concordance invariants. The
706:
703:
384:
675:
722:
20:
642:
454:
111:
699:
391:
is also a concordance invariant. A subtler concordance invariant are the
357:
353:
16:
Link equivalence relation weaker than isotopy but stronger than homotopy
453:. In this case one considers two submanifolds concordant if there is a
376:
A function of a link that is invariant under concordance is called a
365:
694:
Livingston, Charles, A survey of classical knot concordance, in:
407:
One can analogously define concordance for any two submanifolds
360:: isotopy implies concordance implies homotopy. A link is a
334:{\displaystyle f(L_{0}\times \{1\})=L_{1}\times \{1\}}
261:{\displaystyle f(L_{0}\times \{0\})=L_{0}\times \{0\}}
587:
548:
504:
463:
413:
274:
201:
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72:
32:
615:
573:
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445:
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98:
58:
188:{\displaystyle f:L_{0}\times \to S^{n}\times }
8:
607:
601:
568:
562:
328:
322:
300:
294:
255:
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227:
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498:i.e., if there is a manifold with boundary
674:
625:This higher-dimensional concordance is a
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431:
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313:
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273:
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161:
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90:
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50:
37:
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7:
446:{\displaystyle M_{0},M_{1}\subset N}
616:{\displaystyle M_{1}\times \{1\}.}
99:{\displaystyle L_{1}\subset S^{n}}
59:{\displaystyle L_{0}\subset S^{n}}
14:
574:{\displaystyle M_{0}\times \{0\}}
535:{\displaystyle W\subset N\times }
529:
517:
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303:
278:
230:
205:
182:
170:
154:
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1:
676:10.1016/S0040-9383(99)00041-5
542:whose boundary consists of
395:, and in fact all rational
364:if it is concordant to the
750:
491:{\displaystyle N\times ,}
696:Handbook of knot theory
617:
575:
536:
492:
447:
372:Concordance invariants
335:
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189:
100:
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618:
576:
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378:concordance invariant
336:
263:
190:
101:
61:
698:, pp 319–347,
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356:, and stronger than
352:. It is weaker than
350:equivalence relation
272:
199:
117:
70:
30:
702:, Amsterdam, 2005.
389:signature of a knot
110:if there exists an
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331:
258:
185:
96:
56:
403:Higher dimensions
393:Milnor invariants
741:
680:
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678:
669:(6): 1253–1289,
658:
622:
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619:
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541:
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457:between them in
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346:link concordance
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217:
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729:Knot invariants
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686:Further reading
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344:By its nature,
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385:linking number
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330:
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316:
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2:
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714:0-444-51452-X
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708:
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664:
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623:
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397:finite type
21:mathematics
723:Categories
649:References
643:Slice knot
362:slice link
195:such that
108:concordant
734:Manifolds
599:×
560:×
515:×
509:⊂
468:×
455:cobordism
438:⊂
320:×
292:×
247:×
219:×
168:×
155:→
137:×
112:embedding
84:⊂
44:⊂
700:Elsevier
663:Topology
637:See also
627:relative
358:homotopy
707:2179265
354:isotopy
712:
366:unlink
348:is an
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