More 3-manifolds with multiple knot-surgery and branched-cover descriptions
Published online by Cambridge University Press: 24 October 2008
Extract
For any integer N ≽ 3 we will construct a 3-manifold which can be described as + 1 surgery on N distinct knots in S3. We will also give examples of 3-manifolds which are N-fold cyclic branched covers of S3 over 2 distinct knots. Brakes (2) discovered the first examples of 3-manifolds with multiple knot surgery descriptions. Our construction is much different and follows directly from the construction used by Lickerish (6) to describe a manifold which has 2 distinct knot surgery descriptions. Giller (5) has given examples of 3-manifolds which arise as cyclic branched covers over distinct knots in S3. Qur construction is similar, but the knots are much easier to distinguish, being iterated torus knots.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 473 - 475
- Copyright
- Copyright © Cambridge Philosophical Society 1982
References
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