CR Structures Of Once-Punctured Torus Bundles

The Cauchy-Riemann geometry (CR in short) is modelled on the three sphere and the group of its biholomorphic transformations. In 2008 Falbel makes use of ideal triangulations to shows that the figure eight knot complement admits a (branched) CR structure. This three manifold belongs to a larger class of important three manifolds that are fiber bundles over the circle, with fiber space the once-punctured torus. In this talk we introduce the audience to these manifolds and show that almost every once-punctured torus bundle admits a (branched) CR structure.