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Dolbeault cohomology of a loop space

Laszlo Lempert·Ning Zhang
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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).

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Laszlo Lempert, Ning Zhang. 2004-03-24. Dolbeault cohomology of a loop space. https://arxiv.org/abs/math/0403405

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