Integral Finite Surgeries on Knots in $S^3$

Abstract

Using the correction terms in Heegaard Floer homology, we prove that if a knot in $S^3$ admits a positive integral $\mathbf{T}$-, $\mathbf{O}$- or $\mathbf{I}$-type surgery, it must have the same knot Floer homology as one of the knots given in our complete list, and the resulting manifold is orientation-preservingly homeomorphic to the $p$-surgery on the corresponding knot.

17 pages. arXiv admin note: text overlap with arXiv:1310.1346 by other authors

References in corpus (5)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Floer homology and knot complements
• Obstructing finite surgery
• Half-integral finite surgeries on knots in $S^3$

Cited by in corpus (3)

• Finite Dehn surgeries on knots in $S^3$
• Surgery obstructions and character varieties
• Knots with Prism Manifold Surgeries