Cauchy-Riemann geometry and contact topology in three dimensions

Details Cauchy-Riemann geometry and contact topology in three dimensions Cauchy-Riemann geometry and contact topology in three dimensions

2000-03-30

arxiv.org/abs/math/0003211v1

Proc. Natl. Sci. Counc. ROC(A), 24(2000),87-94

Mathematics

Differential Geometry

22 pages,review paper

Scientific paper

We introduce a global Cauchy-Riemann($CR$)-invariant and discuss its behavior on the moduli space of $CR$-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.

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