Teichmüller Theory and the Universal Period Mapping via Quantum Calculus and the $H^{1/2}$ Space on the Circle

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dc.creatorNag, Subhashis
dc.creatorSullivan, Dennis
dc.date1993-10-07
dc.date1993-10-08
dc.date.accessioned2026-07-07T08:57:48Z
dc.date.available2026-07-07T08:57:48Z
dc.descriptionThe Universal Teichmüller Space, $T(1)$, is a universal parameter space for all Riemann surfaces. In earlier work of the first author it was shown that one can canonically associate infinite- dimensional period matrices to the coadjoint orbit manifold $Diff(S^1)/Mobius(S^1)$ -- which resides within $T(1)$ as the (Kirillov-Kostant) submanifold of ``smooth points'' of $T(1)$. We now extend that period mapping $Π$ to the entire Universal Teichmüller space utilizing the theory of the Sobolev space $H^{1/2}(S^1)$. $Π$ is an equivariant injective holomorphic immersion of $T(1)$ into Universal Siegel Space, and we describe the Schottky locus utilizing Connes' ``quantum calculus''. There are connections to string theory. Universal Teichmüller Space contains also the separable complex submanifold $T(H_\infty)$ -- the Teichmüller space of the universal hyperbolic lamination. Genus-independent constructions like the universal period mapping proceed naturally to live on this completion of the classical Teichmüller spaces. We show that $T(H_\infty)$ carries a natural convergent Weil-Petersson pairing.
dc.description39 pages (TEX)
dc.identifierhttps://arxiv.org/abs/alg-geom/9310005
dc.identifierhttp://arxiv.org/abs/alg-geom/9310005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/147071
dc.subjectAlgebraic Geometry
dc.subjectFunctional Analysis
dc.subjectHigh Energy Physics - Theory
dc.titleTeichmüller Theory and the Universal Period Mapping via Quantum Calculus and the $H^{1/2}$ Space on the Circle
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