Cauchy-Riemann geometry and contact topology in three dimensions

2000/03/30 by Jih-Hsin Cheng
Mathematics · #math.DG #math.SG #msc:57R17 #msc:32V05 #msc:53D35

paper · pdf

published as Proc. Natl. Sci. Counc. ROC(A), 24(2000),87-94 · 22 pages,review paper

arxiv created 2000/03/30 · arxiv updated 2009/11/30

Abstract

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.

Related

• Contact topology and CR geometry in three dimensions
• The topology and geometry of contact structures in dimension three
• Contact structures, CR Yamabe invariant, and connected sum
• The space of Cauchy-Riemann structures on 3-D compact contact manifolds
• Monopoles and contact 3-manifolds