Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

Details Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

2007-03-29

arxiv.org/abs/math/0703869v3

Math. Ann. 342 (2008), no. 2, 405--447.

Mathematics

Symplectic Geometry

Scientific paper

10.1007/s00208-008-0241-4

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold.

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