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

Coronal lines and the importance of deep core-valence correlation in Ag-like ions

We report on large-scale and critically evaluated {\em ab initio} MCDHF calculations of the wavelength of the "coronal", M1 transition $4f\ ^2\mathrm{F}_{5/2}^o-^2\mathrm{F}_{7/2}^o$in Ag-like ions. The transition between these two fine structure levels, which makes up the ground term for$Z \ge 62$in the isoelectronic sequence, has recently been observed in Yb$^{23+}$and W$^{27+}$, where the latter could be of great importance for fusion plasma diagnostics. We present recommended values for all members of the sequence between$Z = 50$and$94$, which are supported by excellent agreement with values from recent experiments. The importance of including core-valence correlation with the$n=3$ shell in the theoretical model is emphasized. The results show close to spectroscopic accuracy for these forbidden lines.Comment: 10 pages, 5 figures, 3 table