Journal of Differential Geometry

Holomorphic Line Bunbles on the loop space of the Riemann Sphere

Ning Zhang

Full-text: Open access

Abstract

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.

Article information

Source
J. Differential Geom., Volume 65, Number 1 (2003), 1-17.

Dates
First available in Project Euclid: 22 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090503051

Digital Object Identifier
doi:10.4310/jdg/1090503051

Mathematical Reviews number (MathSciNet)
MR2057529

Citation

Zhang, Ning. Holomorphic Line Bunbles on the loop space of the Riemann Sphere. J. Differential Geom. 65 (2003), no. 1, 1--17. doi:10.4310/jdg/1090503051. https://projecteuclid.org/euclid.jdg/1090503051


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