2001/07/24 by Suhyoung Choi, Choi, Suhyoung
Mathematics · #53A20 #53C15 #57M50 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.GR #math.GT #math.RA #msc:53A20 #msc:53C15 #msc:57M50
paper · pdf · doi:10.48550/arxiv.math/0107172
35 pages
openalex publication_date 2001/07/24 · arxiv created 2003/07/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Σ is locally homeomorphic to the space of representations of the orbifold fundamental group of Σ to G following the work of Thurston, Morgan, and Lok. This implies that the deformation space of (G, X)-structures on Σ is locally homeomorphic to the space of representations of the orbifold fundamental group to G when restricted to the region of proper conjugation action by G.