Geometric analysis demonstrates a holomorphic immersion of the oper holonomy map on surfaces, indicating an extension of symplectic structures beyond standard projective geometry.
In this paper, we construct the moduli space of marked oper structures on a closed, oriented smooth surface of negative Euler characteristic as a holomorphic fiber bundle over Teichmüller space. We prove that the holonomy map from the space of marked oper structures to the moduli space of reductive flat bundles is a holomorphic immersion, generalizing the known results for the moduli space of marked complex projective structures. Finally, we prove that the symplectic structure on the moduli space of marked complex projective structures extends to a pre-symplectic structure on the moduli space of marked opers whose reduced phase space is the space of marked complex projective structures.
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Andrew Sanders (2018) studied this question.
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