The paper computes the second group cohomology of complex deformations of the circle, identifies extending cocycles including a relative one with rotation number and conformal radius, and proves Virasoro uniformization for Segal moduli spaces.
Quasiconformal T eichm \"u ller theory as an analytical foundation for two-dimensional conformal field theory
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Complex deformations of the circle: Group cohomology and Virasoro uniformization
The paper computes the second group cohomology of complex deformations of the circle, identifies extending cocycles including a relative one with rotation number and conformal radius, and proves Virasoro uniformization for Segal moduli spaces.