Geometric Structures on Orbifolds and Holonomy Representations |
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Authors: | Suhyoung Choi |
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Affiliation: | (1) Department of Mathematics, College of Natural Sciences, Seoul National University, 151–742 Seoul, Korea |
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Abstract: | An orbifold is a topological space modeled on quotient spaces of a finite group actions. We can define the universal cover of an orbifold and the fundamental group as the deck transformation group. Let G be a Lie group acting on a space X. We show that the space of isotopy-equivalence classes of (G, X)-structures on a compact orbifold is locally homeomorphic to the space of representations of the orbifold fundamental group of to G following the work of Thurston, Morgan, and Lok. This implies that the deformation space of (G, X)-structures on is locally homeomorphic to the character variety of representations of the orbifold fundamental group to G when restricted to the region of proper conjugation action by G. |
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Keywords: | deformation space geometric structure group representation orbifold |
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