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String Bracket and Flat Connections
Let be a flat principal bundle over a closed and oriented
manifold of dimension . We construct a map of Lie algebras \Psi:
\H_{2\ast} (L M) \to {\o}(\Mc), where \H_{2\ast} (LM) is the even
dimensional part of the equivariant homology of , the free loop space of
, and \Mc is the Maurer-Cartan moduli space of the graded differential Lie
algebra \Omega^\ast (M, \adp), the differential forms with values in the
associated adjoint bundle of . For a 2-dimensional manifold , our Lie
algebra map reduces to that constructed by Goldman in \cite{G2}. We treat
different Lie algebra structures on \H_{2\ast}(LM) depending on the choice of
the linear reductive Lie group in our discussion.Comment: 28 pages. This is the final versio
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