A hyperbolic 3-manifold M carries a flat PSL2(ℂ)-connection whose Chern-Simons invariant has been much studied since the early 1980s. For example, its real part is the volume of M. Explicit formulas in terms of a triangulation involve the dilogarithm. In joint work with Andy Neitzke we use 3-dimensional spectral networks to abelianize the computation of complex Chern-Simons invariants. The locality of the classical Chern-Simons invariant, expressed in the language of topological field theory, plays an important role.
This video is part of Harvard University‘s conference JDG 2017.
