Holomorphic line bundles on the loop space of the Riemann sphere

Ning Zhang, Purdue University

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

COinS