On the number of finite $p/q$-surgeries
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- by Margaret I. Doig PDF
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Abstract:
We study finite, non-cyclic knot surgeries, that is, surgeries which give manifolds of finite but not cyclic fundamental group. These manifolds are known to be knot surgeries except for the dihedral manifolds. We show that, for a fixed $p$, there are finitely many dihedral manifolds that are $p/q$-surgery, and we place a bound on which manifolds they may be. In the process, we calculate a recursive relationship among the Heegaard Floer d-invariants of dihedral manifolds with a given first homology and calculate a bound on which d-invariants would occur if such a manifold were surgery on a knot in $S^3$.References
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Additional Information
- Margaret I. Doig
- Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
- Received by editor(s): November 4, 2013
- Received by editor(s) in revised form: February 3, 2015, June 4, 2015, and June 12, 2015
- Published electronically: October 20, 2015
- Communicated by: Martin Scharlemann
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2205-2215
- MSC (2010): Primary 51M09, 57M25, 57R65
- DOI: https://doi.org/10.1090/proc/12865
- MathSciNet review: 3460179