Dolbeault cohomology of a loop space
classification
🧮 math.CV
math-phmath.DGmath.MP
keywords
spacecohomologydolbeaultloopcomplexcomputeconsistingdimensional
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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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