265:
221:
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128:
339:
595:
552:
494:
451:
377:
186:
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398:
Alternatively, one can relax this definition by dropping the requirement that the surface be properly embedded. Suppose now that
634:, volume 43 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, Providence, R.I., 1980.
191:
17:
133:
618:
43:
639:
A construction of 3-manifolds whose homeomorphism classes of
Heegaard splittings have polynomial growth
101:
665:
318:
577:
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433:
359:
168:
294:
270:
649:
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403:
51:
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40:
28:
whose topology cannot be made simpler by a certain type of operation known as
55:
25:
260:{\displaystyle \alpha \cap \beta =\partial \alpha =\partial \beta }
597:
and there does not exist a boundary-compressing disk for
426:
in an essential arc (one that does not cobound a disk in
406:(with boundary) embedded in the boundary of a 3-manifold
24:
is a two-dimensional surface within a three-dimensional
609:
is boundary-incompressible by the second definition.
580:
537:
479:
436:
362:
321:
297:
273:
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104:
589:
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527:is the closure of a small annular neighborhood of
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445:
371:
333:
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279:
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496:or there exists a boundary-compressing disk for
379:or there exists a boundary-compressing disk for
469:is said to be boundary-compressible if either
356:is a disk that cobounds a ball with a disk in
216:{\displaystyle \alpha \cup \beta =\partial D}
8:
519:embedded in the boundary of a solid torus
457:is called a boundary-compressing disk for
579:
536:
478:
435:
361:
320:
296:
272:
228:
193:
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158:{\displaystyle D\cap \partial M=\beta }
74:are a subset of the interior points of
7:
566:is not contained in the interior of
632:Lectures on Three-Manifold Topology
581:
538:
480:
437:
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251:
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14:
645:(1992), no. 4, 653–674.
414:is a properly embedded disk in
123:{\displaystyle D\cap S=\alpha }
66:is a subset of the boundary of
62:, meaning that the boundary of
22:boundary-incompressible surface
325:
1:
558:is not properly embedded in
508:is boundary-incompressible.
334:{\displaystyle \partial (S}
311:does not cobound a disk in
70:and the interior points of
682:
590:{\displaystyle \partial V}
547:{\displaystyle \partial V}
489:{\displaystyle \partial M}
446:{\displaystyle \partial S}
372:{\displaystyle \partial M}
181:{\displaystyle \partial D}
80:boundary-compressing disk
410:. Suppose further that
90:is defined to be a disk
18:low-dimensional topology
393:boundary-incompressible
304:{\displaystyle \alpha }
287:is an essential arc in
280:{\displaystyle \alpha }
619:Incompressible surface
591:
562:since the interior of
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447:
373:
335:
305:
281:
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124:
54:with boundary that is
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350:boundary-compressible
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306:
282:
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218:
183:
160:
125:
578:
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434:
430:with another arc in
360:
319:
315:with another arc in
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271:
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102:
46:. Suppose also that
30:boundary compression
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331:
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120:
641:, Osaka J. Math.
511:For instance, if
56:properly embedded
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129:
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681:
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574:is embedded in
533:
532:
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404:compact surface
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52:compact surface
12:
11:
5:
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637:T. Kobayashi,
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623:
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586:
583:
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540:
504:. Otherwise,
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387:. Otherwise,
368:
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348:is said to be
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3:
2:
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629:
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569:
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541:
530:
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473:is a disk in
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328:
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117:
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44:with boundary
42:
38:
33:
31:
27:
23:
19:
642:
638:
631:
606:
602:
598:
571:
570:. However,
567:
563:
559:
555:
528:
524:
520:
517:trefoil knot
512:
510:
505:
501:
497:
470:
466:
465:. As above,
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458:
454:
427:
423:
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411:
407:
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397:
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388:
384:
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353:
349:
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344:The surface
343:
312:
288:
165:are arcs in
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71:
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63:
59:
47:
36:
34:
29:
21:
15:
422:intersects
625:References
418:such that
352:if either
98:such that
41:3-manifold
666:Manifolds
630:W. Jaco,
582:∂
539:∂
481:∂
453:). Then
438:∂
364:∂
323:∂
299:α
275:α
255:β
252:∂
246:α
243:∂
237:β
234:∩
231:α
208:∂
202:β
199:∪
196:α
173:∂
153:β
144:∂
141:∩
118:α
109:∩
660:Category
613:See also
35:Suppose
26:manifold
650:1192734
554:, then
188:, with
267:, and
605:, so
515:is a
402:is a
50:is a
39:is a
523:and
130:and
82:for
78:. A
20:, a
601:in
531:in
500:in
461:in
391:is
383:in
341:).
94:in
86:in
58:in
16:In
662::
647:MR
643:29
395:.
223:,
32:.
652:.
607:S
603:V
599:S
585:V
572:S
568:V
564:S
560:V
556:S
542:V
529:K
525:S
521:V
513:K
506:S
502:M
498:S
484:M
471:S
467:S
463:M
459:S
455:D
441:S
428:S
424:S
420:D
416:M
412:D
408:M
400:S
389:S
385:M
381:S
367:M
354:S
346:S
329:S
326:(
313:S
291:(
289:S
249:=
240:=
211:D
205:=
176:D
150:=
147:M
138:D
115:=
112:S
106:D
96:M
92:D
88:M
84:S
76:M
72:S
68:M
64:S
60:M
48:S
37:M
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