Publication Date:
1993-01-01
Description:
LetΓbe a Fuchsian group acting on the upper half-planeUand having signature{p,n,0;v1,v2,…,vn};2p−2+∑j=1n(1−1vj)〉0.LetT(Γ)be the Teichmüller space ofΓ. Then there exists a vector bundleℬ(T(Γ))of rank3p−3+noverT(Γ)whose fibre over a pointt∈T(Γ)representingΓtis the space of bounded quratic differentialsB2(Γt)forΓt. LetHom(Γ,G)be the set of all homomorphisms fromΓinto the Mbius groupG.For a given(t,ϕ)∈ℬ(T(Γ))we get an equivalence class of projective structures and a conjugacy class of a homomorphismx∈Hom(Γ,G). Therefore there is a well defined mapΦ:ℬ(T(Γ))→Hom(Γ,G)/G,Φis called the monodromy map. We prove that the monromy map is hommorphism. The casen=0gives the previously known result by Earle, Hejhal Hubbard.
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
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