3D–3D correspondence from Seifert fibering operators

Persistent laminations from Seifert surfaces

We show how an incompressible Seifert surface F for a knot K in S can be used to create an essential lamination LF in the complement of each of an in nite class of knots associated to F . This lamination is persistent for these knots; it remains essential under all non-trivial Dehn llings of the knot complement. This implies a very strong form of Property P for each of these knots.

On Fibering Spheres by Toruses

Knot Adjacency and Fibering

It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of knot adjacency can be used to obtain obstructions to fibering of knots and of 3-manifolds. As an application, given a fibered knot K′, we construct infinitely many non-fibered knots that share the...

Criteria for Virtual Fibering

We prove that an irreducible 3-manifold whose fundamental group satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber dodecahedral space and the Bianchi groups. Moreover, we show that a taut sutu...

Vector operators in the BMN correspondence

We consider a BMN operator with one scalar, φ and one vector, DμZ, impurity field and compute the anomalous dimension both at planar and torus levels. This mixed operator corresponds to a string state with two creation operators which belong to different SO(4) sectors of the background. The anomalous dimension at both levels is found to be the same as the scalar impurity BMN operator. At planar...