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We are interested in studying low-dimensional manifolds and geometric structures on the manifolds and associated representations of the fundamental groups into Lie groups. The basic questions here are on the existences and deformation spaces of geometric structures on manifolds. This study helps us in studying the representations of discrete groups in Lie groups. The study of representations of the fundamental groups of surfaces into Lie groups are of great importance. We have worked on PGL(3,R)-representations using elementary geometric methods. Classically SL(2,R)-representation spaces correspond to the study of Teichmüller spaces. Goldman generalized this study into many more Lie groups and Hitchin worked out many topological properties of semi-simple Lie group representations. Currently, our work has been significantly generalized into PGL(n,R)-representations for n > 3 and into other reductive groups by Labourie and Berger-Wienhard, and so on. In particular, we know that there are components of representations spaces which consist of discrete representations only. Currently, we are interested in 2-dimensional orbifold fundamental group representations into Lie groups.
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arxiv(2022)
semanticscholar(2021)
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Bulletin of the Brazilian Mathematical Society, New Seriesno. 1 (2019): 243-291
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