Determinant Bundles, Quillen Metrics, and Mumford Isomorphisms over the UniversalCommensurability Teichmueller Space

摘要

A coherent, genus-independent, equivariant construction of determinant linebundles, and connecting Mumford isomorphisms, is obtained over the inductive limit of the Teichmueller spaces of Riemann surfaces of varying genus. The direct limit of the Teichmueller spaces corresponds to the inverse limit over the directed system of all finite unbranched coverings of a fixed surface.