In this talk, we will introduce the Fock-Goncharov Coordinates on the moduli space $\mathcal{T}^+_3\left(S_{g,n}\right)$ of framed convex real projective structures on a punctured surface $S\left(=S_{g,n}\right)$ of negative Euler characteristic and show that it is canonically homeomorphic with $\mathbb{R}^{8\big|\chi (S)\big|}_{>0}$.



Prerequisite: Linear Algebra, Surface Topology


Flag, Triple and quadruple ratio, framing
References


[FG07]     V. V. Fock and A. B. Goncharov. Moduli spaces of convex projective structures on surfaces. Adv. Math. 208(1):249-273, 2007.

[CTT20]   Alex Casella, Dominic Tate, and Stephan Tillmann. Moduli spaces of real projective structures on surfaces volume 38 of MSJ Memoirs. Mathematical Society of Japan, Tokyo, [2020] ©2020.
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