Finite knot surgeries and Heegaard Floer homology

Doig, Margaret I¹

¹Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, NY 13244-1150, USA

Algebraic and Geometric Topology, Tome 15 (2015) no. 2, pp. 667-690

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.667

Classification : 57M25, 57R65
Keywords: knot surgery, finite surgery, Heegaard Floer, correction term, $d$–invariant

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