Multi(de)grafting quasi-Fuchsian complex projective structures via bubbles

Abstract

We show that the simultaneous (de)grafting of a complex projective structure with quasi-Fuchsian holonomy along a multicurve can be performed by a simple sequence of one bubbling and one debubbling. As a consequence we obtain that any complex projective structure with quasi-Fuchsian holonomy $\rho :{\pi }_1(S)\to$ PSL${}_2\mathbb{C}$ can be joined to the corresponding uniformizing structure ${\sigma }_{\rho }$ by a simple sequence of one bubbling and one debubbling, with a stopover in the space of branched complex projective structures.

19 pages, 9 pictures

References in corpus (1)

• Bubbling complex projective structures with quasi-Fuchsian holonomy

Cited by in corpus (3)

• Bubbling complex projective structures with quasi-Fuchsian holonomy
• Local deformations of branched projective structures: Schiffer variations and the Teichmüller map
• Tame and relatively elliptic ${\mathbb{CP}}^1$-structures on the thrice-punctured sphere