Constructing Lefschetz Fibrations with Arbitrary Slope
We prove that for any rational number $r\in (2,8)$, there exists a genus-$g$ Lefschetz fibration over the two-sphere with large enough genus-$g$ having the slope is $r$.
math.GT↗
arXiv subjects
Adalet Cengel
Publications and source records attributed to Adalet Cengel.
Low-slope Lefschetz fibrations
For $g\geq 3$, we construct genus-$g$ Lefschetz fibrations over the two-sphere whose slopes are arbitrarily close to $2$. The total spaces of the Lefschetz fibrations can be chosen to be minimal and simply connected. It is also shown that the infimum and the supremum of slopes all Lefschetz fibrations are not realized as slopes.
math.GT↗