The oriented graph of multi-graftings in the Fuchsian case

Abstract

We prove the connectedness and calculate the diameter of the oriented graph of graftings associated to exotic complex projective structures on a compact surface S with a given holonomy representation of Fuchsian type. The oriented graph of graftings is the graph whose vertices are the equivalence classes of marked CP^1-structures on S with a given fixed holonomy, and there is an oriented edge between two structures if the second is obtained from the first by grafting.

Improved version. The paper chaged title: from "The oriented graph of graftings..." to "The oriented graph of multi-graftings..."

References in corpus (2)

• Branched projective structures with quasi-Fuchsian holonomy
• Some Graftings of Complex Projective Structures with Schottky Holonomy

Cited by in corpus (7)

• 2 π-grafting and complex projective structures, I
• Bubbling complex projective structures with quasi-Fuchsian holonomy
• Multi(de)grafting quasi-Fuchsian complex projective structures via bubbles
• 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
• On Thurston's parametrization of $\mathbb{C}{\mathrm{P}}^1$-structures
• 2π-grafting and complex projective structures with generic holonomy