2015/09/17 by Sergiu Moroianu, Moroianu, Sergiu · 1 citation
Mathematics · Physics and Astronomy · #58J28 #Advanced Operator Algebra Research #Crystallography and Radiation Phenomena #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Noncommutative and Quantum Gravity Theories #math.DG #msc:58J28
paper · pdf · doi:10.48550/arxiv.1509.05156
Survey, 16 pages
arxiv created 2015/09/17 · openalex publication_date 2015/09/17 · arxiv updated 2015/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Chern-Simons invariants of closed oriented Riemannian 3-manifolds are introduced and studied from the basics. Their first-order variation is the Cotton tensor. The properties of the Cotton tensor: symmetry, conformal covariance, trace- and divergence-freedom, are recovered as corollaries of the Chern-Simons invariant. We prove that the Cotton tensor is the obstruction to local conformal flatness in dimension 3. Finally we discuss the link between Chern-Simons invariants, the eta invariant, and the central value of the Selberg zeta function. This is a survey paper without original results, based on lecture notes for a doctoral course at the University of Bucharest, March 2014.