Finite knot surgeries and Heegaard Floer homology

Doig, Margaret I

doi:10.2140/agt.2015.15.667

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Finite knot surgeries and Heegaard Floer homology

Margaret I Doig

Algebraic & Geometric Topology 15 (2015) 667–690

DOI: 10.2140/agt.2015.15.667

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 $π_{1} (Y)$ finite and $| H_{1} (Y) | \leq 4$ , we classify the manifolds which are knot surgery and the knot surgeries which give them; for $| H_{1} (Y) | \leq 32$ , 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

Volume 15, issue 2 (2015)