2012/07/04 by David Radnell, Eric Schippers, Radnell, David +3 · 1 citation
Mathematics · Physics and Astronomy · #30C62 #30F60 (Primary) 30C55 #32G15 #46E20 #81T40 (Secondary) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Holomorphic and Operator Theory #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #hep-th #math-ph #math.CV #math.MP #msc:30C55 #msc:30C62 #msc:30F60 #msc:32G15 #msc:46E20 #msc:81T40
paper · pdf · doi:10.48550/arxiv.1207.0973
43 pages
arxiv created 2012/07/04 · openalex publication_date 2012/07/04 · arxiv updated 2012/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider bordered Riemann surfaces which are biholomorphic to compact Riemann surfaces of genus g with n regions biholomorphic to the disc removed. We define a refined Teichmueller space of such Riemann surfaces and demonstrate that in the case that 2g+2-n>0, this refined Teichmueller space is a Hilbert manifold. The inclusion map from the refined Teichmueller space into the usual Teichmueller 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 Teichmueller space by a properly discontinuous group of biholomorphisms.