All Exceptional Surgeries on Alternating Knots Are Integral Surgeries
نویسنده
چکیده
We show that all exceptional surgeries on hyperbolic alternating knots in the 3-sphere are integral surgeries.
منابع مشابه
On Knot Floer Homology and Lens Space Surgeries
In an earlier paper, we used the absolute grading on Heegaard Floer homology HF to give restrictions on knots in S which admit lens space surgeries. The aim of the present article is to exhibit stronger restrictions on such knots, arising from knot Floer homology. One consequence is that all the non-zero coefficients of the Alexander polynomial of such a knot are ±1. This information in turn ca...
متن کاملInvolutive Heegaard Floer Homology
Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to Z4-equivariant Seiberg-Witten Floer homology. Further, we obtain two new invariants of homology cobordism, d and d̄, and two invariants of smooth knot concordance, V 0 and V 0. We also develop a formula for the involutive Heeg...
متن کاملThe Classification of Toroidal Dehn Surgeries on Montesinos Knots
Exceptional Dehn surgeries have been classified for 2-bridge knots and Montesinos knots of length at least 4. In this paper we classify all toroidal Dehn surgeries on Montesinos knots of length 3.
متن کاملSmall Seifert fibered surgery on hyperbolic pretzel knots
The study of exceptional surgery on hyperbolic knots has been well developed over the last quarter century. One particularly well studied problem is that of exceptional surgery on arborescent knots, which include Montesinos knots and pretzel knots. Thanks to the positive solution to the Geometrization conjecture [Per03a, Per03b, Per03c], any exceptional surgery is either reducible, toroidal, or...
متن کاملNon-integral Toroidal Dehn Surgeries
If we perform a non-trivial Dehn surgery on a hyperbolic knot in the 3-sphere, the result is usually a hyperbolic 3-manifold. However, there are exceptions: there are hyperbolic knots with surgeries that give lens spaces [1], small Seifert fiber spaces [2], [5], [7], [20], and toroidal manifolds, that is, manifolds containing (embedded) incompressible tori [6], [7]. In particular, Eudave-Muñoz ...
متن کامل