scholarly journals Meromorphic projective structures, grafting and the monodromy map

2021 ◽  
Vol 383 ◽  
pp. 107673
Author(s):  
Subhojoy Gupta ◽  
Mahan Mj
Keyword(s):  
Projective Structures ◽  
Monodromy Map

scholarly journals On monodromy map

1993 ◽  
Vol 16 (4) ◽  
pp. 695-708
Author(s):  
Jharna D. Sengupta
Keyword(s):  
Vector Bundle ◽  
Conjugacy Class ◽  
Equivalence Class ◽  
Half Plane ◽  
Fuchsian Group ◽  
Teichmüller Space ◽  
Teichmuller Space ◽  
Projective Structures ◽  
Upper Half Plane ◽  
Monodromy Map

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.

scholarly journals Symplectic geometry of the moduli space of projective structures in homological coordinates

2017 ◽  
Vol 210 (3) ◽  
pp. 759-814 ◽  
Author(s):  
Marco Bertola ◽  
Dmitry Korotkin ◽  
Chaya Norton
Keyword(s):  
Moduli Space ◽  
Symplectic Geometry ◽  
Projective Structures

Analysis of \mathbb{C}P^{N-1} sigma models via projective structures

Nonlinearity ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 1-36 ◽  
Author(s):  
S Post ◽  
A M Grundland
Keyword(s):  
Sigma Models ◽  
Projective Structures

Projective structures on open surfaces

1983 ◽  
pp. 36-47 ◽  
Author(s):  
Daniel M. Gallo ◽  
R. Michael Porter
Keyword(s):  
Projective Structures
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