Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds
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...
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| Veröffentlicht in: | Transformation groups 2023-06, Vol.28 (2), p.639-693 |
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| creator | CHOI, SUHYOUNG JUNG, HONGTAEK |
| description | 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. |
| doi_str_mv | 10.1007/s00031-022-09789-7 |
| format | Article |
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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.</description><identifier>ISSN: 1083-4362</identifier><identifier>EISSN: 1531-586X</identifier><identifier>DOI: 10.1007/s00031-022-09789-7</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Coordinates ; Deformation ; Lie Groups ; Mathematics ; Mathematics and Statistics ; Topological Groups</subject><ispartof>Transformation groups, 2023-06, Vol.28 (2), p.639-693</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-283b2c2f7c9802ceeb61e49172f40e136b9d686a26938111336d67ad2fc9f9303</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00031-022-09789-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00031-022-09789-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>CHOI, SUHYOUNG</creatorcontrib><creatorcontrib>JUNG, HONGTAEK</creatorcontrib><title>Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds</title><title>Transformation groups</title><addtitle>Transformation Groups</addtitle><description>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.</description><subject>Algebra</subject><subject>Coordinates</subject><subject>Deformation</subject><subject>Lie Groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Topological Groups</subject><issn>1083-4362</issn><issn>1531-586X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKt_wNWA6-hNMs1jKfUJhQpVcBdmMolOaSdjkhH7700dwZ2r-zrfuXAQOidwSQDEVQQARjBQikEJqbA4QBMyy6uZ5K-HuQfJcMk4PUYnMa4BiOCcT5Be7bb9xprUmmLufWjarko2Fr4r0rstbqzzYVulNs-rvjL7i8vC7tN-FU_Br_fkpy1WKQwmDWEkKV6GunV-08RTdOSqTbRnv3WKXu5un-cPeLG8f5xfL7ChAhKmktXUUCeMkkCNtTUntlREUFeCJYzXquGSV5QrJgkhjPGGi6qhziinGLApuhh9--A_BhuTXvshdPmlphnggtGSZBUdVSb4GIN1ug_ttgo7TUDvg9RjkDoHqX-C1CJDbIRiFndvNvxZ_0N9A9t6deI</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>CHOI, SUHYOUNG</creator><creator>JUNG, HONGTAEK</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230601</creationdate><title>Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds</title><author>CHOI, SUHYOUNG ; JUNG, HONGTAEK</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-283b2c2f7c9802ceeb61e49172f40e136b9d686a26938111336d67ad2fc9f9303</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Coordinates</topic><topic>Deformation</topic><topic>Lie Groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Topological Groups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>CHOI, SUHYOUNG</creatorcontrib><creatorcontrib>JUNG, HONGTAEK</creatorcontrib><collection>CrossRef</collection><jtitle>Transformation groups</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>CHOI, SUHYOUNG</au><au>JUNG, HONGTAEK</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds</atitle><jtitle>Transformation groups</jtitle><stitle>Transformation Groups</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>28</volume><issue>2</issue><spage>639</spage><epage>693</epage><pages>639-693</pages><issn>1083-4362</issn><eissn>1531-586X</eissn><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.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00031-022-09789-7</doi><tpages>55</tpages></addata></record> |
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| subjects | Algebra Coordinates Deformation Lie Groups Mathematics Mathematics and Statistics Topological Groups |
| title | Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds |
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