Abstract
Let S be a subset of n points on a compact connected oriented surface M of genus g , and let G be a compact semisimple Lie group. The space of isomorphism classes of flat G -connections on P : = M ∖ S with fixed conjugacy class of monodromy around each point of S will be denoted by R . It is known that R has a natural symplectic structure. We relate R with the space of geodesic ( 4 g + n ) -gons in G . A natural 2-form on the space of geodesic ( 4 g + n ) -gons is constructed using the Killing form on Lie ( G ) . We establish an identity between the symplectic form on R and this 2-form on geodesic ( 4 g + n ) -gons in G .
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