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A Hilbert manifold structure on the Weil-Petersson class Teichmuller space of bordered Riemann surfaces
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Communications in Contemporary Mathematics, ISSN 0219-1997, Vol. 17, no 4, 1550016Article in journal (Refereed) Published
Abstract [en]

We consider bordered Riemann surfaces which are biholomorphic to compact Riemann surfaces of genus g with n regions biholomorphic to the disk removed. We define a refined Teichmuller space of such Riemann surfaces (which we refer to as the WP-class Teichmuller space) and demonstrate that in the case that 2g + 2 - n > 0, this refined Teichmuller space is a Hilbert manifold. The inclusion map from the refined Teichm " uller space into the usual Teichm " uller space (which is a Banach manifold) is holomorphic. We also show that the rigged moduli space of Riemann surfaces with non-overlapping holomorphic maps, appearing in conformal field theory, is a complex Hilbert manifold. This result requires an analytic reformulation of the moduli space, by enlarging the set of non-overlapping mappings to a class of maps intermediate between analytically extendible maps and quasiconformally extendible maps. Finally, we show that the rigged moduli space is the quotient of the refined Teichmuller space by a properly discontinuous group of biholomorphisms.

Place, publisher, year, edition, pages
2015. Vol. 17, no 4, 1550016
Keyword [en]
Rigged moduli space, Weil-Petersson class Teichmuller space
National Category
URN: urn:nbn:se:uu:diva-258737DOI: 10.1142/S0219199715500169ISI: 000356791900009OAI: oai:DiVA.org:uu-258737DiVA: diva2:842579
Available from: 2015-07-21 Created: 2015-07-20 Last updated: 2016-02-17Bibliographically approved

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Staubach, Wolfgang
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Analysis and Probability Theory
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