Dolbeault cohomology of a loop space

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2004Embargo end date: 01 Mar 2004 English Publisher:International Press of BostonJournal:Acta Mathematica, volume 193, pages 241-268 (issn: 0001-5962,

Copyright policy )Funded by:NSF | Research in Several Compl...

Authors: Lempert, László; Zhang, Ning;

doi: 10.1007/bf02392565 , 10.48550/arxiv.math/0403405

arXiv: math/0403405

Dolbeault cohomology of a loop space

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Abstract

The loop space LP_1 of the Riemann sphere is an infinite dimensional complex manifold consisting of maps (loops) from S^1 to P_1 in some fixed C^k or Sobolev W^{k,p} space. In this paper we compute the Dolbeault cohomology groups H^{0,1}(LP_1).

26 pages

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Keywords

Manifolds of mappings, Mathematics - Differential Geometry, Mathematics - Complex Variables, FOS: Physical sciences, Mathematical Physics (math-ph), Questions of holomorphy and infinite-dimensional manifolds, Complex manifolds, Differential Geometry (math.DG), 58B12, 32Q99, 58D15, loop spaces, Dolbeault cohomology, FOS: Mathematics, Complex Variables (math.CV), \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Mathematical Physics

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