Small knots and large handle additions

We construct a hyperbolic 3-manifold $M$ (with $\partial M$ totally geodesic) which contains no essential closed surfaces, but for any even integer $g> 0$ there are infinitely many separating slopes $r$ on $\partial M$ so that $M[r]$, the 3-manifold obtained by attaching 2-handle to $M$ along $r$, contains an essential separating closed surface of genus $g$ and is still hyperbolic. The result contrasts sharply with those known finiteness results for the cases $g=0,1$. Our 3-manifold $M$ is the complement of a simple small knot in a handlebody.Comment: 25 pages, 14 figure

Handle additions producing essential surfaces

We construct a small, hyperbolic 3-manifold $M$ such that, for any integer $g\geq 2$, there are infinitely many separating slopes $r$ in $\partial M$ so that $M(r)$, the 3-manifold obtained by attaching a 2-handle to $M$ along $r$, is hyperbolic and contains an essential separating closed surface of genus $g$. The result contrasts sharply with those known finiteness results on Dehn filling, and it also contrasts sharply with the known finiteness result on handle addition for the cases $g=0,1$. Our 3-manifold $M$ is the complement of a hyperbolic, small knot in a handlebody of genus 3.Comment: 28 pages, 22 figure

A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus

Let $M$ be an orientable 3-manifold with $\partial M$ a single torus. We show that the number of boundary slopes of immersed essential surfaces with genus at most $g$ is bounded by a quadratic function of $g$. In the hyperbolic case, this was proved earlier by Hass, Rubinstein and Wang.Comment: 11 pages, 1 figur

Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields

We investigate the dependence of charge transfer on the intensity of driving laser field when SiO2 crystal is irradiated by an 800 nm laser. It is surprising that the direction of charge transfer undergoes a sudden reversal when the driving laser intensity exceeds critical values with different carrier envelope phases. By applying quantum-trajectory analysis, we find that the Bloch oscillation plays an important role in charge transfer in solid. Also, we study the interaction of strong laser with gallium nitride (GaN) that is widely used in optoelectronics. A pump-probe scheme is applied to control the quantum trajectories of the electrons in the conduction band. The signal of charge transfer is controlled successfully by means of theoretically proposed approach