Margaret I. Doig
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 $S^3$.
Journal: Proceedings of the American Mathematical Society
DOI: 10.1090/proc/12865