A Hilbert manifold structure on the Weil-Petersson class Teichmüller space of bordered Riemann surfaces
2015 (English)In: Communications in Contemporary Mathematics, ISSN 0219-1997Article in journal (Refereed) Published
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 Teichmüller space of such Riemann surfaces (which we refer to as the WP-class Teichmüller space) and demonstrate that in the case that 2g + 2 − n > 0, this refined Teichmüller space is a Hilbert manifold. The inclusion map from the refined Teichmüllerspace into the usual Teichmüller space (which is a Banach manifold) is holomorphic. We also show that the rigged moduli space of Riemann surfaces with non-overlappingholomorphic 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 mapsand quasiconformally extendible maps. Finally we show that the rigged moduli space is thequotient of the refined Teichmüller space by a properly discontinuous group of biholomorphisms.
Place, publisher, year, edition, pages
World Scientific, 2015.
Geometry Other Physics Topics
IdentifiersURN: urn:nbn:se:uu:diva-285996OAI: oai:DiVA.org:uu-285996DiVA: diva2:921410