#### Volume 15, issue 2 (2015)

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Finite knot surgeries and Heegaard Floer homology

### Margaret I Doig

Algebraic & Geometric Topology 15 (2015) 667–690
##### 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 ${Spin}^{c}$ structures. For ${\pi }_{1}\left(Y\right)$ finite and $|{H}_{1}\left(Y\right)|\le 4$, we classify the manifolds which are knot surgery and the knot surgeries which give them; for $|{H}_{1}\left(Y\right)|\le 32$, we classify the manifolds which are surgery and place restrictions on the surgeries which may give them.

##### Keywords
knot surgery, finite surgery, Heegaard Floer, correction term, $d$–invariant
Primary: 57M25
Secondary: 57R65
##### Publication
Revised: 7 March 2014
Accepted: 19 May 2014
Published: 22 April 2015
##### Authors
 Margaret I Doig Department of Mathematics Syracuse University 215 Carnegie Building Syracuse, NY 13244-1150 USA