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Contents
1. Introduction
2. Symplectic group, Lagrangians
3. Invariants of Lagrangian subspaces
4. Moduli spaces of framed and decorated local systems
5. Local systems on quivers and their framings
6. $\mathcal {X}$-coordinates for maximal representations
7. Topology of the space of maximal framed representations
8. Singularities of the space of framed maximal representations into $Sp(4,\mathbf {R})$
9. General $\mathcal {X}$-coordinates
10. $\mathcal {X}$-coordinates for representations into isogenic groups
11. $\mathcal {A}$-coordinates for decorated local systems
A. Normal form for pair of quadratic forms