Holomorphic line bundles on the loop space of the Riemann sphere
Abstract
The loop space L[special characters omitted] of the Riemann sphere consisting of all Ck or Sobolev Wk,p maps S 1 → [special characters omitted] is an infinite dimensional complex manifold. The loop space of the group of Möbius Transformations is a Lie group, denoted by LPGL (2,[special characters omitted]), which acts naturally on L[special characters omitted]. In this thesis we completely clarify LPGL(2,[special characters omitted]) invariant holomorphic line bundles on L[special characters omitted]. Further, we prove that the space of holomorphic sections of any such line bundle is finite dimensional, and compute the dimension for a generic bundle.
Degree
Ph.D.
Advisors
Lempert, Purdue University.
Subject Area
Mathematics
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