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On the number of finite $ p/q$-surgeries


Author: Margaret I. Doig
Journal: Proc. Amer. Math. Soc. 144 (2016), 2205-2215
MSC (2010): Primary 51M09, 57M25, 57R65
DOI: https://doi.org/10.1090/proc/12865
Published electronically: October 20, 2015
MathSciNet review: 3460179
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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$.


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Additional Information

Margaret I. Doig
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244

DOI: https://doi.org/10.1090/proc/12865
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
Article copyright: © Copyright 2015 American Mathematical Society

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