Dehn surgeries on knots in product manifolds

@article{Ni2011DehnSO,
  title={Dehn surgeries on knots in product manifolds},
  author={Yi Ni},
  journal={Journal of Topology},
  year={2011},
  volume={4}
}
  • Yi Ni
  • Published 28 January 2010
  • Mathematics
  • Journal of Topology
We show that if a surgery on a knot in a product sutured manifold yields the same product sutured manifold, then this knot is a 0‐ or 1‐crossing knot. The proof uses techniques from sutured manifold theory. 
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References

SHOWING 1-10 OF 21 REFERENCES
Dehn surgeries that yield fibred 3-manifolds
We study Dehn surgeries on null-homotopic knots that yield fibred 3-manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai’s theory of sutured…
Knots and Links
Introduction Codimension one and other matters The fundamental group Three-dimensional PL geometry Seifert surfaces Finite cyclic coverings and the torsion invariants Infinite cyclic coverings and…
Knot Floer homology detects genus-one fibred knots
Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on contact topology and Gabai's theory of sutured manifold…
Surgery on a knot in (Surface x I)
Suppose F is a compact orientable surface, K is a knot in F x I, and N is the 3-manifold obtained by some non-trivial surgery on K. If F x {0} compresses in N, then there is an annulus in F x I with…
Surgery on knots in solid tori
A norm for the homology of 3-manifolds
On construit une norme naturelle aisement calculable sur l'homologie des 3-varietes. Cette norme est une extension de la notion de genre d'un nœud
Knots are determined by their complements
This answers a question apparently first raised by Tietze [T, p. 83]. It was previously known that there were at most two knots with a given complement [CGLS, Corollary 3]. The notion of equivalence…
1-bridge braids in solid tori
FOLIATIONS AND THE TOPOLOGY OF 3-MANIFOLDS. II
In this paper and its continuation [3] we investigate the following question: Let M be a compact oriented irreducible 3-manifold whose boundary is a torus. If TV is obtained by filling dM along an…
Foliations and the topology of 3-manifolds
In this announcement we discuss the close relationship between the topology of 3-manifolds and the foliations that is possesses. We will introduce and state the main result, then use it and the ideas…
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