Given a pants decomposition $\mathcal{ PC} = \{ \gamma_1, \ldots, \gamma_{ \xi}\}$ on a hyperbolizable surface $\Sigma$ and a vector $\underline{ c} = (c_1, \ldots, c_{ \xi}) \in \mathbb{ R}_+^\xi$, we describe a plumbing construction which endows $\Sigma$ with a complex projective structure for which the associated holonomy representation $\rho$ is quasi-Fuchsian and for which $\ell_\rho(\gamma_i) = c_i$. When $\underline{ c} \to \underline{ 0} = (0, \ldots, 0)$ this construction limits to Kra's plumbing construction. In addition, when $\Sigma = \Sigma_{ 1,1}$, the holonomy representations of these structures belong to the `linear slice' of quasi-Fuchsian space $\mathrm{ QF}(\Sigma)$ defined by Komori and Parkonnen. We discuss some conjectures for these slices suggested by the pictures we created in joint work with Yamashita.
Categories: math.GT