Gluing formulas for volume forms on representation varieties of surfaces

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dc.authorid0000-0003-1223-3007
dc.contributor.authorErdal, Esma Diricanen_US
dc.date.accessioned2025-09-19T07:59:00Z
dc.date.available2025-09-19T07:59:00Z
dc.date.issued2025-08-06
dc.departmentIşık Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.departmentIşık University, Faculty of Engineering and Natural Sciences, Department of Mathematicsen_US
dc.description.abstractLet Σg,n be a compact oriented surface of genus g≥4 with n boundary components. Due to Witten, the twisted Reidemeister torsion coincides with a power of the Atiyah–Bott–Goldman–Narasimhan symplectic form on the space of representations of π1(Σg,0) in any semi-simple Lie group. In the present paper, we first obtain a multiplicative gluing formula for the twisted Reidemeister torsion of Σg,0 in terms of torsions of Σg1,1,Σg2,1, and boundary circle S1, where g=g1+g2 and g1,g2≥2. Then, by using Heusener and Porti’s results on Σg,n, we show that the symplectic volume form on the representation variety of Σg,0 can be expressed as a product of the holomorphic symplectic volume forms on the relative representation varieties of surfaces Σg1,1 and Σg2,1.en_US
dc.description.sponsorshipITU-DOSAPen_US
dc.description.versionPublisher's Version
dc.identifier.citationErdal, E. D. (2025). Gluing formulas for volume forms on representation varieties of surfaces. Beitrage zur Algebra und Geometrie. https://doi.org/10.1007/s13366-025-00801-1en_US
dc.identifier.doi10.1007/s13366-025-00801-1
dc.identifier.issn0138-4821
dc.identifier.issn2191-0383
dc.identifier.scopus2-s2.0-105012777408
dc.identifier.scopusqualityQ3
dc.identifier.urihttps://hdl.handle.net/11729/6710
dc.identifier.urihttps://doi.org/10.1007/s13366-025-00801-1
dc.identifier.wosWOS:001545113400001
dc.identifier.wosqualityQ4
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakEmerging Sources Citation Index (ESCI)en_US
dc.institutionauthorErdal, Esma Diricanen_US
dc.institutionauthorid0000-0003-1223-3007
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherSpringer Natureen_US
dc.relation.ispartofBeitrage zur Algebra und Geometrieen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectReidemeister torsionen_US
dc.subjectRepresentation varietyen_US
dc.subjectVolume formen_US
dc.subjectTorsionen_US
dc.subjectSpacesen_US
dc.titleGluing formulas for volume forms on representation varieties of surfacesen_US
dc.typeArticleen_US
dspace.entity.typePublicationen_US

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