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Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds

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Title
Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds
Author(s)
Choi, Suhyoung; Hongtaek Jung
Publication Date
2023-06
Journal
Transformation Groups, v.28, no.2, pp.639 - 693
Publisher
Birkhauser
Abstract
Let O be a closed orientable 2-orbifold of negative Euler characteristic. Huebschmann constructed the Atiyah-Bott-Goldman type symplectic form ω on the deformation space C(O) of convex projective structures on O. We show that the deformation space C(O) of convex projective structures on O admits a global Darboux coordinate system with respect to ω. To this end, we show that C(O) can be decomposed into smaller symplectic spaces. In the course of the proof, we also study the deformation space C(O) for an orbifold O with boundary and construct the symplectic form on the deformation space of convex projective structures on O with fixed boundary holonomy. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
URI
https://pr.ibs.re.kr/handle/8788114/13354
DOI
10.1007/s00031-022-09789-7
ISSN
1083-4362
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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