Abstract
It is well known that any 3-manifold can be obtained by Dehn surgery on a link, but not which ones can be obtained from a knot or which knots can produce them. We investigate these two questions for elliptic Seifert fibered spaces (other than lens spaces) using the Heegaard Floer correction terms or d -invariants associated to a 3-manifold Y and its torsion Spinc structures. For π1(Y) finite and |H1(Y)| ≤ 4, we classify the manifolds which are knot surgery and the knot surgeries which give them; for |H1(Y)| ≤ 32, we classify the manifolds which are surgery and place restrictions on the surgeries which may give them. © 2015, Algebraic & Geometric Topology. All rights reserved.