• Corpus ID: 43352494

# Thurston norm and cosmetic surgeries

```@article{Ni2011ThurstonNA,
title={Thurston norm and cosmetic surgeries},
author={Yi Ni},
journal={arXiv: Geometric Topology},
year={2011}
}```
• Yi Ni
• Published 22 January 2010
• Mathematics, Medicine
• arXiv: Geometric Topology
Two Dehn surgeries on a knot are called cosmetic if they yield homeomorphic manifolds. For a null-homologous knot with certain conditions on the Thurston norm of the ambient manifold, if the knot admits cosmetic surgeries, then the surgery coefficients are equal up to sign.

## References

SHOWING 1-10 OF 16 REFERENCES
Nonseparating spheres and twisted Heegaard Floer homology
If a 3–manifold Y contains a nonseparating sphere, then some twisted Heegaard Floer homology of Y is zero. This simple fact allows us to prove several results about Dehn surgery on knots in such
Knots, sutures, and excision
• Mathematics
• 2008
We develop monopole and instanton Floer homology groups for balanced sutured manifolds, in the spirit of [12]. Applications include a new proof of Property P for knots.
Holomorphic disks and topological invariants for closed three-manifolds
• Mathematics
• 2001
The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y, equipped with a Spiny structure. Given a Heegaard splitting of Y = U 0o U Σ U 1 , these
Manifolds with small Heegaard Floer ranks
• Mathematics
• 2010
We show that the only irreducible three-manifold with positive first Betti number and Heegaard Floer homology of rank two is homeomorphic to zero-framed surgery on the trefoil. We classify links
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
Knot Floer homology and rational surgeries
• Mathematics
• 2010
Let K be a rationally null-homologous knot in a three-manifold Y . We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold
Monopoles and Three-Manifolds
• Mathematics
• 2008
Preface 1. Outlines 2. The Seiberg-Witten equations and compactness 3. Hilbert manifolds and perturbations 4. Moduli spaces and transversality 5. Compactness and gluing 6. Floer homology 7.
Cosmetic Surgery in Integral Homology \$L\$-Spaces
Let \$K\$ be a non-trivial knot in \$S^3\$, and let \$r\$ and \$r'\$ be two distinct rational numbers of same sign, allowing \$r\$ to be infinite; we prove that there is no orientation-preserving homeomorphism
Floer homology and knot complements
We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call CF_r. It