Volume 15, issue 2 (2015)

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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 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.

Keywords
knot surgery, finite surgery, Heegaard Floer, correction term, $d$–invariant
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57R65
References
Publication
Received: 9 July 2012
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