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More 3-manifolds with multiple knot-surgery and branched-cover descriptions

Published online by Cambridge University Press:  24 October 2008

Charles Livingston
Charles Livingston
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana47405
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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

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References

REFERENCES

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