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

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
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