IMCS/Publications/BASM/Issues/BASM n.2 (78), 2015/

The Cotton tensor and Chern-Simons invariants in dimension 3: an introduction

Authors: Sergiu Moroianu


We review, with complete proofs, the theory of Chern-Simons invariants for oriented Riemannian 3-manifolds. The Cotton tensor is the first-order variation of the Chern-Simons invariant. We deduce that it is conformally invariant, and trace- and divergence-free, from the corresponding properties of the Chern-Simons invariant. Moreover, the Cotton tensor vanishes if and only if the metric is locally conformally flat. In the last part of the paper we survey the link of Chern-Simons invariants with the eta invariant and with the central value of the Selberg zeta function of odd type.

Institutul de Matematică al Academiei Române
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