Monodromy groups and linearly polymorphic functions

The symplectic nature of the space of projective connections on Riemann surfaces

“…We begin by recalling the basic terminology to be used in this article; for more information, see [3], [12], [14]- [16] and [26, pp. 291-295, 343-346].…”

“…For this purpose we introduce the Teichm~ller space 7(/') (of the marked Fuchsian group F) and the universal Teichmi~ller curve V(F), a natural fiber space over T(F) with projection ~: V(F) ---} T(F). The fundamental properties of the mapping F are: (i) although the set Hom(F, PSL(2,1I~))/PSL(2, C) has in general rather complicated singularities, the points in ImF are regular points of that space (see [9]- [10], [12], El4] and [16]), and (ii) the mapping F is a local biholomorphism from the space Q onto an open subset of Hom(F, PSL(2,~))/PSL(2,1E) (see [3], [14] and [16]). 5].…”

“…(For details, refer to [2], [17] and [26,Chap. For more information on the mapping F, the reader is referred to [5], [7], [12], [14] and [26, pp. See also Sect.…”

The oriented graph of multi-graftings in the Fuchsian case

“…Grafting was used by Hejhal [5,Theorem 4] and Thurston (unpublished) to produce examples of projective structures with holonomy ρ that are different from the uniformizing structure σ u = ρ(Γ g )\H 2 . Such structures are called exotic.…”

Projective structures, grafting and measured laminations

“…A second, more synthetic geometric description of P.S/ is due to Thurston, and proceeds through the operation of grafting-a construction which traces its roots back at least to Klein [25,Section 50], with a modern history developed by many authors (Maskit [27], Hejhal [19], Sullivan-Thurston [41], Goldman [18], Gallo-KapovichMarden [15], Tanigawa [42], McMullen [29] and Scannell-Wolf [36]). The simplest example of grafting may be described as follows.…”