Loading...
Please wait, while we are loading the content...
Similar Documents
Only integral Dehn surgeries can yield reducible manifolds
| Content Provider | Scilit |
|---|---|
| Author | Gordon, C. McA. Luecke, J. |
| Copyright Year | 1987 |
| Description | Let K be a knot in S3, and let K(a/b) denote the closed oriented 3-manifold obtained by a/b-Dehn surgery on K. (We parametrize the Dehn surgeries on K by ℚ ∩ {1/0} as in [9]; in particular, K(1/0) = S3.) If K is a (p, q)-cable knot, then K(pq) is always reducible (see Section 3), and it is conjectured by González-Acuña and Short in [5] that these are the only examples where Dehn surgery on a knot in S3 yields a reducible manifold. One of the results in this direction proved in [5] is that if π1 (K(a/b)) is a non-trivial free product then |b| ≤ 5. We show that this may be sharpened to the assertion in the title. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6453897351AFACFE2991721E7F89AB13/S0305004100067086a.pdf/div-class-title-only-integral-dehn-surgeries-can-yield-reducible-manifolds-div.pdf |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100067086 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 01 |
| Volume Number | 102 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1987-07-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Condensed Matter Physics Dehn Surgery |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
