Translator Disclaimer
October, 2003 Holomorphic Line Bunbles on the loop space of the RiemannSphere
Ning Zhang
J. Differential Geom. 65(1): 1-17 (October, 2003). DOI: 10.4310/jdg/1090503051


The loop space L1 of the Riemann sphere consisting of all Ck or Sobolev Wk,p maps S1 → ℙ1 is an infinite dimensional complex manifold. The loop group LPGL(2,ℂ) acts on L1. We prove that the group of LPGL(2, ℂ) invariant holomorphic line bundles on L1 is isomorphic to an infinite dimensional Lie group. 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.


Download Citation

Ning Zhang. "Holomorphic Line Bunbles on the loop space of the RiemannSphere." J. Differential Geom. 65 (1) 1 - 17, October, 2003.


Published: October, 2003
First available in Project Euclid: 22 July 2004

MathSciNet: MR2057529
Digital Object Identifier: 10.4310/jdg/1090503051

Rights: Copyright © 2003 Lehigh University


Vol.65 • No. 1 • October, 2003
Back to Top