Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle.

Kuranishi's fundamental result (1962) associates to any compact complex manifold X 0 {X_{0}} a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to X 0 {X_{0}}. In this paper, we give an analogous statement for Levi-flat CR-manifolds fibering properly over the circle by associating to any such 𝒳 0 {\mathcal{X}_{0}} the loop space of a finite-dimensional analytic space which serves as a local moduli space of CR-structures close to 𝒳 0 {\mathcal{X}_{0}}. We then develop in this context a Kodaira–Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples. [ABSTRACT FROM AUTHOR]