Cauchy-Riemann geometry and contact topology in three dimensions
arXiv:math/0003211
Abstract
We introduce a global Cauchy-Riemann()-invariant and discuss its behavior on the moduli space of -structures. We argue that this study is related to the Smale conjecture in 3-topology and the problem of counting complex structures. Furthermore, we propose a contact-analogue of Ray-Singer's analytic torsion. This ``contact torsion'' is expected to be able to distinguish among ``contact lens'' spaces. We also propose the study of a certain kind of monopole equation associated with a contact structure.
22 pages,review paper