The Hilbert-uniformization is real-analytic

Simple item page
dc.creatorEbert, Johannes F.
dc.creatorFriedrich, Roland M.
dc.date2006-01-16
dc.date.accessioned2026-07-07T06:58:57Z
dc.date.available2026-07-07T06:58:57Z
dc.descriptionIn \cite{Boed}, C.-F. Bödigheimer constructed a finite cell-complex $\mf{Par}_{g,n,m}$ and a bijective map $\cH: \mf{Dip}_{g,n,m} \to \mf{Par}_{g,n,m}$ (the Hilbert-uniformization) from the moduli space of dipole functions on Riemann surfaces with $n$ directions and $m$ punctures to $\mf{Par}_{g,n,m}$. In \cite{Boed} and \cite{Eb}, it is proven that $\cH$ is a homeomorphism. The first result of this note is that the space $\mf{Dip}_{g,n,m}$ carries a natural structure of a real-analytic manifold. Our second result is that $\cH$ is real-analytic, at least on the preimage of the top-dimensional open cells of $\mf{Par}_{g,n,m}$.
dc.descriptionNote; 7 pages
dc.identifierhttps://arxiv.org/abs/math/0601378
dc.identifierhttp://arxiv.org/abs/math/0601378
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107568
dc.subjectDifferential Geometry
dc.subjectCombinatorics
dc.subject14H15; 32Q30
dc.titleThe Hilbert-uniformization is real-analytic
dc.typetext

Files

Collections

arXiv